A371871 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k-2,n-3*k).
1, 0, 1, 5, 18, 66, 246, 924, 3493, 13277, 50697, 194327, 747319, 2882061, 11142027, 43167573, 167561586, 651513594, 2537041938, 9892847952, 38623197264, 150959213886, 590626854072, 2312979822738, 9065733950526, 35561306875380, 139595183125750
Offset: 0
Keywords
Programs
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Maple
A371871 := proc(n) 1/(1-x^3)/(1-x)^(n-1) ; coeftayl(%,x=0,n) ; end proc: seq(A371871(n),n=0..60) ; # R. J. Mathar, Apr 22 2024
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PARI
a(n) = sum(k=0, n\3, binomial(2*n-3*k-2, n-3*k));
Formula
a(n) = [x^n] 1/((1-x^3) * (1-x)^(n-1)).
D-finite with recurrence 9*n*a(n) +3*(-17*n+16)*a(n-1) +3*(21*n-50)*a(n-2) +(-17*n+16)*a(n-3) +10*(2*n-5)*a(n-4)=0. - R. J. Mathar, Apr 22 2024