Geodesic
Plane sections of the generalised Pascal pyramid and their interpretations
Diskretnaya Matematika, Tome 22 (2010) no. 3, pp. 83-93 
O. V. Kuzmin; M. V. Seregina. Plane sections of the generalised Pascal pyramid and their interpretations. Diskretnaya Matematika, Tome 22 (2010) no. 3, pp. 83-93. http://geodesic.mathdoc.fr/item/DM_2010_22_3_a7/
@article{DM_2010_22_3_a7,
     author = {O. V. Kuzmin and M. V. Seregina},
     title = {Plane sections of the generalised {Pascal} pyramid and their interpretations},
     journal = {Diskretnaya Matematika},
     pages = {83--93},
     year = {2010},
     volume = {22},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_3_a7/}
}
TY  - JOUR
AU  - O. V. Kuzmin
AU  - M. V. Seregina
TI  - Plane sections of the generalised Pascal pyramid and their interpretations
JO  - Diskretnaya Matematika
PY  - 2010
SP  - 83
EP  - 93
VL  - 22
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/DM_2010_22_3_a7/
LA  - ru
ID  - DM_2010_22_3_a7
ER  - 
%0 Journal Article
%A O. V. Kuzmin
%A M. V. Seregina
%T Plane sections of the generalised Pascal pyramid and their interpretations
%J Diskretnaya Matematika
%D 2010
%P 83-93
%V 22
%N 3
%U http://geodesic.mathdoc.fr/item/DM_2010_22_3_a7/
%G ru
%F DM_2010_22_3_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider sums of elements of plane sections of the generalised Pascal pyramide. We evaluate the sums and find recurrence relations which these sums obey, and then suggest enumerative interpretations of the combinatorial objects under investigation.

[1] Kuzmin O. V, Obobschennye piramidy Paskalya i ikh prilozheniya, Nauka, Novosibirsk, 2000 | MR

[2] Čerin Z., “Sums of squares and products of Jacobsthal numbers”, J. Integer Sequences, 10:2 (2007), 07.2.5 | MR | Zbl

[3] Feinberg M., “Fibonacci–Tribonacci”, Fibonacci Q., 1 (1963), 71–74

[4] Shannon A. G., “Tribonacci numbers and Pascal's pyramid”, Fibonacci Q., 15 (1977), 268–275 | MR | Zbl