A190154 Diagonal sums of the triangle A190152.

1, 1, 2, 11, 30, 91, 303, 936, 2936, 9300, 29209, 91917, 289547, 911218, 2868341, 9029949, 28424456, 89477119, 281667368, 886657081, 2791106585, 8786130132, 27657838272, 87064082194, 274068969337, 862741399379, 2715822822365, 8549136143060, 26911817257385

Offset

0,3

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..500

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-4*k,3*n-6*k).

Conjecture: G.f. ( -1+x+x^3-x^4+2*x^2 ) / ( (x^3-3*x^2+4*x-1)*(x^3+3*x^2+2*x+1) ). - R. J. Mathar, Mar 15 2013

Maple

seq(add(binomial(3*n-4*k, 3*n-6*k), k=0..floor(n/2)), n=0..20);

Mathematica

Table[Sum[Binomial[3n-4k, 3n-6k], {k, 0, n/2}], {n, 0, 28}]

Prog

(Maxima) makelist(sum(binomial(3*n-4*k, 3*n-6*k), k, 0, n/2), n, 0, 28);
(PARI) for(n=0, 30, print1(sum(k=0, floor(n/2), binomial(3*n-4*k, 3*n-6*k)), ", ")) \\ G. C. Greubel, Dec 30 2017

Crossrefs

Cf. A190152, A190153.

Sequence in context: A023622 A119438 A094005 * A187830 A115058 A158295

Adjacent sequences: A190151 A190152 A190153 * A190155 A190156 A190157

Keyword

nonn,easy

Author

Emanuele Munarini, May 05 2011

Status

approved