A174792 Expansion of x*(1 - x^2)/(1 - x + 7*x^2 + x^3).

0, 1, 1, -7, -15, 33, 145, -71, -1119, -767, 7137, 13625, -35567, -138079, 97265, 1099385, 556609, -7236351, -12231999, 37865849, 130726193, -122102751, -1075051951, -351058887, 7296407521, 10828871681, -39894922079, -122993431367, 145442151505, 1046291093153

Offset

0,4

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (1,-7,-1).

Formula

G.f.: (1/2)*(x/(1 - x))*g(f(x)), where f(x) = (1 + x)/(-1 + x), and g(x) = (1-x^2)/(1 - x^2 - x^3) is the g.f. of the Padovan sequence A000931.

a(n) = a(n-1) - 7*a(n-2) - a(n-3), n >= 4. - Franck Maminirina Ramaharo, Jan 06 2019

Mathematica

CoefficientList[Series[x*(1 - x^2)/(1 - x + 7*x^2 + x^3), {x, 0, 50}], x]

Prog

(Maxima) (a[0] : 0, a[1] : 1, a[2] : 1, a[3] : -7, a[n] := a[n-1] - 7*a[n-2] - a[n-3], makelist(a[n], n, 0, 50)); /* Franck Maminirina Ramaharo, Jan 06 2019 */

Crossrefs

Cf. A000931

Sequence in context: A014001 A291642 A271995 * A063592 A159792 A247606

Adjacent sequences: A174789 A174790 A174791 * A174793 A174794 A174795

Keyword

sign,easy,less

Author

Roger L. Bagula, Mar 29 2010

Extensions

Edited by Franck Maminirina Ramaharo, Jan 06 2019

Status

approved