A392543 Expansion of 1 / ((1-x)^2 - x^7).

1, 2, 3, 4, 5, 6, 7, 9, 13, 20, 31, 47, 69, 98, 136, 187, 258, 360, 509, 727, 1043, 1495, 2134, 3031, 4288, 6054, 8547, 12083, 17114, 24279, 34475, 48959, 69497, 98582, 139750, 198032, 280593, 397629, 563624, 799116, 1133190, 1607014, 2278870, 3231319, 4581397

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,1).

Formula

a(n) = Sum_{k=0..floor(n/7)} binomial(n-5*k+1,n-7*k).

a(n) = 2*a(n-1) - a(n-2) + a(n-7).

Mathematica

CoefficientList[Series[1/((1-x)^2-x^7), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 17 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec(1/((1-x)^2-x^7))
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! 1 / ((1-x)^2 - x^7)); // Vincenzo Librandi, Jan 17 2026

Crossrefs

Cf. A005709, A049017, A392544, A392545, A392546, A392547.

Sequence in context: A085793 A281809 A143286 * A160339 A033072 A030287

Adjacent sequences: A392540 A392541 A392542 * A392544 A392545 A392546

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 15 2026

Status

approved