A generalization of Pascal’s triangle using powers of base numbers
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.

@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/}
}
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 843962 | Zbl 0598.05011

[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 0792.05001

[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 0863.05006

[5] John E. Freund Restricted occupancy theory – a generalization of Pascal’s triangle, Amer. Math. Monthly, Volume 63 (1956), pp. 20-27 | Article | MR 74356 | Zbl 0070.01201

[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 0886.05003

[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, http://www.research.att.com/~njas/sequences/ (Internet Database)