A098182 a(n) = 3*a(n-1) - a(n-2) + a(n-3), a(0)=1,a(1)=1,a(2)=3.

1, 1, 3, 9, 25, 69, 191, 529, 1465, 4057, 11235, 31113, 86161, 238605, 660767, 1829857, 5067409, 14033137, 38861859, 107619849, 298030825, 825334485, 2285592479, 6329473777, 17528163337, 48540608713, 134423136579

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

G.f. : (1-x)^2/(1-3*x+x^2-x^3).

a(n) = Sum_{k=0..floor(n/2)} binomial(n+k, 3*k) * 2^k.

Mathematica

CoefficientList[Series[(1 - x)^2/(1 - 3 x + x^2 - x^3), {x, 0, 50}], x] (* G. C. Greubel, Mar 03 2017 *)

Prog

(PARI) x='x+O(x^50); Vec((1-x)^2/(1-3*x+x^2-x^3)) \\ G. C. Greubel, Mar 03 2017

Crossrefs

Cf. A098183, A098184.

Sequence in context: A211288 A206727 A211296 * A211300 A211293 A211291

Adjacent sequences: A098179 A098180 A098181 * A098183 A098184 A098185

Keyword

easy,nonn

Author

Paul Barry, Aug 30 2004

Status

approved