A373654 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-5*k-1,k).
1, 1, 1, 1, 3, 5, 7, 12, 21, 34, 55, 92, 153, 251, 414, 686, 1133, 1869, 3088, 5103, 8427, 13917, 22990, 37975, 62721, 103598, 171121, 282646, 466852, 771119, 1273690, 2103796, 3474913, 5739647, 9480387, 15659094, 25864698, 42721676, 70564951, 116554700, 192517665
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,2,0,0,-1).
Crossrefs
Cf. A373639.
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(2*n-5*k-1, k));
Formula
G.f.: 1 / (1 - x/(1 - x^3)^2).
a(n) = a(n-1) + 2*a(n-3) - a(n-6) for n > 6.