Annales Mathématiques
Blaise Pascal
no. 1
A generalization of Pascal’s triangle using powers of base numbers
Gábor Kallós1
1 Department of Computer Science Széchenyi István University Egyetem tér 1 Győr, H-9026 HUNGARY
Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 1, pp. 1-15.

In this paper we generalize the Pascal triangle and examine the connections among the generalized triangles and powering integers respectively polynomials. We emphasize the relationship between the new triangles and the Pascal pyramids, moreover we present connections with the binomial and multinomial theorems.

DOI : 10.5802/ambp.211

Gábor Kallós 1

1 Department of Computer Science Széchenyi István University Egyetem tér 1 Győr, H-9026 HUNGARY 
@article{AMBP_2006__13_1_1_0,
     author = {G\'abor Kall\'os},
     title = {A generalization of {Pascal{\textquoteright}s} triangle using powers of base numbers},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {1--15},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {13},
     number = {1},
     year = {2006},
     doi = {10.5802/ambp.211},
     mrnumber = {2233009},
     zbl = {1172.11302},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.211/}
}
TY  - JOUR
AU  - Gábor Kallós
TI  - A generalization of Pascal’s triangle using powers of base numbers
JO  - Annales mathématiques Blaise Pascal
PY  - 2006
SP  - 1
EP  - 15
VL  - 13
IS  - 1
PB  - Annales mathématiques Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.211/
DO  - 10.5802/ambp.211
LA  - en
ID  - AMBP_2006__13_1_1_0
ER  - 
%0 Journal Article
%A Gábor Kallós
%T A generalization of Pascal’s triangle using powers of base numbers
%J Annales mathématiques Blaise Pascal
%D 2006
%P 1-15
%V 13
%N 1
%I Annales mathématiques Blaise Pascal
%U https://ambp.centre-mersenne.org/articles/10.5802/ambp.211/
%R 10.5802/ambp.211
%G en
%F AMBP_2006__13_1_1_0
Gábor Kallós. A generalization of Pascal’s triangle using powers of base numbers. Annales mathématiques Blaise Pascal, Tome 13 (2006) no. 1, pp. 1-15. doi : 10.5802/ambp.211. https://ambp.centre-mersenne.org/articles/10.5802/ambp.211/

[1] Mary Basil Pascal’s pyramid, Math. Teacher, Volume 61 (1968), pp. 19-21

[2] Richard C. Bollinger A note on Pascal-T triangles, multinomial coefficients, and Pascal pyramids, The Fibonacci Quarterly, Volume 24.2 (1986), pp. 140-144 | MR | Zbl

[3] Boris A. Bondarenko Generalized Pascal triangles and pyramids, their fractals, graphs and applications, The Fibonacci Association, Santa Clara, 1993 (Translated from russian by Richard C. Bollinger) | Zbl

[4] Sven J. Cyvin; Jon Brunvoll; Bjørg N. Cyvin Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, Volume 34 (1996), pp. 109-121 | Zbl

[5] John E. Freund Restricted occupancy theory – a generalization of Pascal’s triangle, Amer. Math. Monthly, Volume 63 (1956), pp. 20-27 | DOI | MR | Zbl

[6] Gábor Kallós Generalizations of Pascal’s triangle (1993) Master thesis (in Hungarian), Eötvös Loránd University, Budapest

[7] Gábor Kallós The generalization of Pascal’s triangle from algebraic point of view, Acta Acad. Paed. Agriensis, Volume XXIV (1997), pp. 11-18 | Zbl

[8] Robert L. Morton Pascal’s triangle and powers of 11, Math. Teacher, Volume 57 (1964), pp. 392-394

[9] Neil J. A. Sloane On-line encyclopedia of integer sequences, 1044.11108 http://www.research.att.com/~njas/sequences/ (Internet Database)

Cité par Sources :