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A190154 Diagonal sums of the triangle A190152. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 18 19:59 EST 2019. Contains 329288 sequences. (Running on oeis4.)