A109972 Diagonal sums of number triangle A109970.

1, 0, 1, 2, 8, 34, 162, 822, 4365, 23956, 134814, 773746, 4511693, 26652346, 159170385, 959412290, 5829083420, 35661048886, 219491344362, 1358204062536, 8444658457530, 52729475008690, 330518562341537, 2078987880103170

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, Journal of Integer Sequences, 19, 2016, #16.3.5.

Formula

a(0) = 1, a(n) = Sum_{k=0..n-1} (k/(n-k))*binomial(3n-4k-1, n-2k), n>0. [corrected by Michel Marcus, Jan 25 2019]

Prog

(PARI) a(n) = if (n==0, 1, sum(k=0, n-1, (k/(n-k))*binomial(3*n-4*k-1, n-2*k))); \\ Michel Marcus, Jan 25 2019

Crossrefs

Sequence in context: A150901 A046649 A174808 * A019023 A343523 A030857

Adjacent sequences: A109969 A109970 A109971 * A109973 A109974 A109975

Keyword

easy,nonn

Author

Paul Barry, Jul 06 2005

Status

approved