A021079 Expansion of 1/((1-x)(1-2x)(1-4x)(1-7x)).

1, 14, 133, 1086, 8253, 60438, 433861, 3080462, 21737485, 152860422, 1072817109, 7520900478, 52691034397, 369016181366, 2583829064677, 18089666698734, 126639120006189, 886519652765670, 6205820820773365

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (14,-63,106,-56).

Formula

a(n) = -(1/18)+(4/5)*2^n-(32/9)*4^n+(343/90)*7^n. [Antonio Alberto Olivares, May 22 2012]

a(0)=1, a(1)=14; for n>1, a(n) = 11*a(n-1) -28*a(n-2) +2^n - 1. - Vincenzo Librandi, Jul 06 2013

a(0)=1, a(1)=14, a(2)=133, a(3)=1086; for n>3, a(n) = 14*a(n-1) -63*a(n-2) +106*a(n-3) -56*a(n-4). - Vincenzo Librandi, Jul 06 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 4 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 06 2013 *)
LinearRecurrence[{14, -63, 106, -56}, {1, 14, 133, 1086}, 20] (* Robert G. Wilson v, Jul 06 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-4*x)*(1-7*x)))); // Vincenzo Librandi, Jul 06 2013
(Magma) I:=[1, 14, 133, 1086]; [n le 4 select I[n] else 14*Self(n-1)-63*Self(n-2)+106*Self(n-3)-56*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 06 2013

Crossrefs

Sequence in context: A113976 A022738 A017269 * A174563 A233467 A164598

Adjacent sequences: A021076 A021077 A021078 * A021080 A021081 A021082

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved