

A121547


Fourth slice along the 12plane in the cube a(m,n,o) = a(m1,n,o) + a(m,n1,o) + a(m,n,o1) for which the first slice is Pascal's triangle (slice read by antidiagonals).


2



0, 0, 1, 0, 4, 4, 0, 10, 20, 10, 0, 20, 60, 60, 20, 0, 35, 140, 210, 140, 35, 0, 56, 280, 560, 560, 280, 56, 0, 84, 504, 1260, 1680, 1260, 504, 84, 0, 120, 840, 2520, 4200, 4200, 2520, 840, 120, 0, 165, 1320, 4620, 9240, 11550, 9240, 4620, 1320, 165, 1980, 7920
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OFFSET

0,5


LINKS

Table of n, a(n) for n=0..56.


FORMULA

a(m1,n,o) + a(m,n1,o) + a(m,n,o1) with initialization values a(1,0,0) = 1 and a(m<>1=0, n>=0, 0>=o) = 0.


EXAMPLE

The second row is 1, 4, 10, 20, 35, 56, 84, 120, 165, 220 = A000292, i.e., Tetrahedral (or pyramidal) numbers: binomial(n+2,3) = n(n+1)(n+2)/6 (core).
The third row is 4, 20, 60, 140, 280, 504, 840, 1320, 1980, 2860 = A033488 = n*(n+1)*(n+2)*(n+3)/6.
The main diagonal is 0, 4, 60, 560, 4200, 27720, 168168, 960960, 5250960, 27713400 = unknown.


PROG

Excel cell formula: =ZS(1)+Z(1)S+Z(15)S where the term Z(15)S refers to a cell in the previous slice (along the dimension 3), i.e., Z(15)S corresponds to +a(m, n, o1).


CROSSREFS

Cf. A003506, A094305, A121306, A119800, A000292, A007318.
Sequence in context: A236922 A021698 A199739 * A028626 A205507 A137862
Adjacent sequences: A121544 A121545 A121546 * A121548 A121549 A121550


KEYWORD

nonn,tabl


AUTHOR

Thomas Wieder, Aug 06 2006


STATUS

approved



