OFFSET
1,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5,-9,10,-5,1).
FORMULA
a(n) = A001687(5*n).
a(n) = Sum_{k=0..floor(n/2)} binomial(n+1+3*k,n-1-2*k).
a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: x*(1-x)^2/((1-x)^5 - x^2).
MATHEMATICA
LinearRecurrence[{5, -9, 10, -5, 1}, {1, 3, 7, 18, 52}, 50] (* Paolo Xausa, Mar 15 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(n+1+3*k, n-1-2*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 03 2024
STATUS
approved