A019742 Expansion of 1/((1-4x)(1-10x)(1-11x)).

1, 25, 431, 6365, 86511, 1117605, 13957591, 170189245, 2038704671, 24092243285, 281680643751, 3265150951725, 37583315950831, 430083097386565, 4897580558961911, 55540052099419805, 627607236896972991

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (25,-194,440).

Formula

a(n) = 2*4^(n+1)/21 +11^(n+2)/7-5*10^(n+1)/3. - R. J. Mathar, Nov 11 2012

a(0)=1, a(1)=25, a(2)=431; for n>2, a(n) = 25*a(n-1) -194*a(n-2) +440*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 21*a(n-1) -110*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 10 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-10*x)*(1-11*x)))); /* or */ I:=[1, 25, 431]; [n le 3 select I[n] else 25*Self(n-1)-194*Self(n-2)+440*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A020448 A203544 A021704 * A019722 A180800 A004346

Adjacent sequences: A019739 A019740 A019741 * A019743 A019744 A019745

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved