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

Olivier Carton, Jean-Michel Couvreur, Martin Delacourt, and Nicolas Ollinger, Linear Recurrence Sequence Automata and the Addition of Abstract Numeration Systems, 15th Int'l Conf. Comb. Words (WORDS 2025) Lecture Notes Comp. Sci. (LNCS Vol. 15729) 70-82. See p. 71.

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) my(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