A077876 Expansion of (1-x)^(-1)/(1-x+2*x^2).

1, 2, 1, -2, -3, 2, 9, 6, -11, -22, 1, 46, 45, -46, -135, -42, 229, 314, -143, -770, -483, 1058, 2025, -90, -4139, -3958, 4321, 12238, 3597, -20878, -28071, 13686, 69829, 42458, -97199, -182114, 12285, 376514, 351945, -401082, -1104971, -302806, 1907137, 2512750, -1301523, -6327022

Offset

0,2

Comments

Row sums of Riordan array (1/(1-x),x(1-2x)). - Paul Barry, Jul 18 2005

Links

Table of n, a(n) for n=0..45.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (2,-3,2).

Formula

a(n) = Sum_{k=0..n} U(k, 1/(2*sqrt(2))(2*sqrt(2))^k. - Paul Barry, Nov 20 2003 [There is a missing parenthesis, but it is not clear where it should be inserted. - N. J. A. Sloane, Feb 08 2015)

a(n) = Sum_{k=2..n-2} A107920(k). - R. J. Mathar, Oct 13 2017

a(n) = Sum_{k=0..floor((n+1)/2)} binomial(n+1-k,k+1)*(-2)^k, n>=0. - Taras Goy, Apr 15 2020

Mathematica

Join[{a=1, b=2}, Table[c=b-2*a+1; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 21 2011 *)

Prog

(PARI) Vec(1/((1-x)*(1-x+2*x^2)) + O(x^75)) \\ Michel Marcus, Feb 08 2015

Crossrefs

Cf. A001045, A107920.

Sequence in context: A249686 A107853 A054758 * A095056 A337557 A186333

Adjacent sequences: A077873 A077874 A077875 * A077877 A077878 A077879

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved