A137357 a(n) = Sum_{k <= n/2 } binomial(n-2k, 3k+1).

0, 1, 2, 3, 4, 5, 7, 12, 23, 44, 80, 138, 230, 379, 629, 1060, 1810, 3109, 5336, 9120, 15521, 26349, 44713, 75949, 129177, 219918, 374521, 637699, 1085401, 1846804, 3141826, 5344988, 9093989, 15474230, 26332515, 44810670, 76253683, 129755543, 220790480

Offset: 0

Author

Don Knuth, Apr 11 2008

Keywords

• nonn
• easy

References

• D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,1).

Crossrefs

Cf. A137356, A137358, A137359, A137360, A137361, A136444.

Programs

Mathematica

LinearRecurrence[{3, -3, 1, 0, 1}, Range[0, 4], 50] (* Paolo Xausa, Mar 17 2024 *)

Formula

G.f.: x*(x-1) / (x^5+x^3-3*x^2+3*x-1). - Colin Barker, Jan 23 2013