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
Links
- Nathaniel Johnston, Table of n, a(n) for n = 0..500
Programs
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Maple
seq(add(binomial(3*n-4*k,3*n-6*k), k=0..floor(n/2)), n=0..20);
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Mathematica
Table[Sum[Binomial[3n-4k,3n-6k],{k,0,n/2}],{n,0,28}] -
Maxima
makelist(sum(binomial(3*n-4*k,3*n-6*k),k,0,n/2),n,0,28);
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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
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