A371872 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-2*k-1,n-3*k).
1, 1, 3, 11, 40, 147, 547, 2055, 7777, 29602, 113204, 434591, 1673821, 6464539, 25026534, 97087873, 377329971, 1468856383, 5726159811, 22351657810, 87350137071, 341726039806, 1338173763288, 5244830032639, 20573285744475, 80761011408961, 317249771957040
Offset: 0
Keywords
Programs
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Maple
A371872 := proc(n) add(binomial(2*n-2*k-1,n-3*k),k=0..floor(n/3)) ; end proc: seq(A371872(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-2*k-1, n-3*k));
Formula
a(n) = [x^n] 1/((1-x-x^3) * (1-x)^(n-1)).
D-finite with recurrence +n*a(n) +(-15*n+14)*a(n-1) +3*(27*n-50)*a(n-2) +2*(-93*n+259)*a(n-3) +24*(7*n-26)*a(n-4) +(-69*n+260)*a(n-5) +10*(2*n-9)*a(n-6)=0. - R. J. Mathar, Apr 22 2024