A078071 Expansion of (1-x)/(1+2*x+2*x^2+2*x^3).

1, -3, 4, -4, 6, -12, 20, -28, 40, -64, 104, -160, 240, -368, 576, -896, 1376, -2112, 3264, -5056, 7808, -12032, 18560, -28672, 44288, -68352, 105472, -162816, 251392, -388096, 599040, -924672, 1427456, -2203648, 3401728, -5251072, 8105984, -12513280, 19316736, -29818880, 46030848

Offset

0,2

Links

Table of n, a(n) for n=0..40.

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

Formula

a(0) = 1, a(1) = -3, a(2) = 4, a(n) = -2*(a(n-1) + a(n-2) + a(n-3)) for n > 2. - Jinyuan Wang, Apr 07 2020

a(n) = (-1)^n*(b(n+1) - b(n+2) - b(n+3) + b(n+4))/2 where b(n) = A077858(n). - Klaus Purath, Sep 22 2025

Prog

(PARI) Vec((1-x)/(1+2*x+2*x^2+2*x^3) + O(x^50)) \\ Jinyuan Wang, Apr 07 2020

Crossrefs

First differences of A077993, A077858.

Sequence in context: A325973 A363289 A019462 * A359789 A084138 A127141

Adjacent sequences: A078068 A078069 A078070 * A078072 A078073 A078074

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved