A137358 a(n) = Sum_{k <= n/2 } binomial(n-2k, 3k+2).

0, 0, 1, 3, 6, 10, 15, 22, 34, 57, 101, 181, 319, 549, 928, 1557, 2617, 4427, 7536, 12872, 21992, 37513, 63862, 108575, 184524, 313701, 533619, 908140, 1545839, 2631240, 4478044, 7619870, 12964858, 22058847, 37533077, 63865592, 108676262, 184929945, 314685488

Offset

0,4

References

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

Links

Table of n, a(n) for n=0..38.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,1).

Formula

a(0)=0, a(1)=0, a(2)=1, a(3)=3, a(4)=6, a(n)=3*a(n-1)-3*a(n-2)+ a(n-3)+ a(n-5). - Harvey P. Dale, Nov 06 2012

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

Mathematica

Table[Sum[Binomial[n-2k, 3k+2], {k, 0, Floor[n/2]}], {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1, 0, 1}, {0, 0, 1, 3, 6}, 50] (* Harvey P. Dale, Nov 06 2012 *)

Crossrefs

Cf. A137356, A137357, A137359, A137360, A137361, A136444.

Sequence in context: A330910 A226239 A209231 * A143963 A139714 A342211

Adjacent sequences: A137355 A137356 A137357 * A137359 A137360 A137361

Keyword

nonn,easy

Author

Don Knuth, Apr 11 2008

Status

approved