A077880 Expansion of (1-x)^(-1)/(1-2*x^2+x^3).

1, 1, 3, 2, 6, 2, 11, -1, 21, -12, 44, -44, 101, -131, 247, -362, 626, -970, 1615, -2565, 4201, -6744, 10968, -17688, 28681, -46343, 75051, -121366, 196446, -317782, 514259, -832009, 1346301, -2178276, 3524612, -5702852, 9227501, -14930315, 24157855, -39088130, 63246026, -102334114

Offset

0,3

Links

Table of n, a(n) for n=0..41.

Index entries for linear recurrences with constant coefficients, signature (1, 2, -3, 1).

Formula

a(n) = (-1)^n*Fibonacci(n-1) + n. - Vladeta Jovovic, Jul 18 2004

a(n) = A001924(-3-n) = 2*a(n-2) - a(n-3) + 1. - Michael Somos, Dec 31 2012

If 0 is prepended then BINOMIAL transform is A079282 with 0 prepended. - Michael Somos, Dec 31 2012

a(n) = (-1)^n * Sum_{k=0..n} binomial(k-2,n-k). - Seiichi Manyama, Aug 14 2024

Example

1 + x + 3*x^2 + 2*x^3 + 6*x^4 + 2*x^5 + 11*x^6 - x^7 + 21*x^8 - 12*x^9 + 44*x^10 + ...

Mathematica

Table[(-1)^n*Fibonacci[n - 1] + n, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 28 2011 *)

Prog

(PARI) {a(n) = fibonacci(1-n) + n} /* Michael Somos, Dec 31 2012 */

Crossrefs

Cf. A000045.

Sequence in context: A065228 A092843 A078589 * A198930 A263353 A248945

Adjacent sequences: A077877 A077878 A077879 * A077881 A077882 A077883

Keyword

sign

Author

N. J. A. Sloane, Nov 17 2002

Status

approved