A025992 Expansion of 1/((1-2x)(1-5x)(1-7x)(1-8x)).

1, 22, 313, 3666, 38493, 377286, 3529681, 31947322, 282198565, 2447183310, 20920905369, 176852694018, 1481626607917, 12322682753494, 101879323774177, 838170485025354, 6867569457133749, 56077266261254238

Offset

0,2

Comments

From Bruno Berselli, May 09 2013: (Start)

a(n)-2*a(n-1), for n>0, gives A019928 (after 1);

a(n)-5*a(n-1), for n>0, gives A016311 (after 1);

a(n)-7*a(n-1), for n>0, gives A016297 (after 1);

a(n)-8*a(n-1), for n>0, gives A016296 (after 1);

a(n)-7*a(n-1)+10*a(n-2), for n>1, gives A016177 (after 15);

a(n)-9*a(n-1)+14*a(n-2), for n>1, gives A016162 (after 13);

a(n)-10*a(n-1)+16*a(n-2), for n>1, gives A016161 (after 12);

a(n)-12*a(n-1)+35*a(n-2), for n>1, gives A016131 (after 10);

a(n)-13*a(n-1)+40*a(n-2), for n>1, gives A016130 (after 9);

a(n)-15*a(n-1)+56*a(n-2), for n>1, gives A016127 (after 7);

a(n)-20*a(n-1)+131*a(n-2)-280*a(n-3), for n>2, gives A000079 (after 4);

a(n)-17*a(n-1)+86*a(n-2)-112*a(n-3), for n>2, gives A000351 (after 25);

a(n)-15*a(n-1)+66*a(n-2)-80*a(n-3), for n>2, gives A000420 (after 49);

a(n)-14*a(n-1)+59*a(n-2)-70*a(n-3), for n>2, gives A001018 (after 64),

and naturally: a(n)-22*a(n-1)+171*a(n-2)-542*a(n-3)+560*a(n-4), for n>3, gives 0 (see Harvey P. Dale in Formula lines). (End)

Links

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

Index entries for linear recurrences with constant coefficients, signature (22,-171,542,-560).

Formula

a(0)=1, a(1)=22, a(2)=313, a(3)=3666, a(n)=22*a(n-1)-171*a(n-2)+ 542*a(n-3)- 560*a(n-4). - Harvey P. Dale, Jan 29 2013

a(n) = (5*8^(n+3)-9*7^(n+3)+5^(n+4)-2^(n+3))/90. - Yahia Kahloune, May 07 2013

Mathematica

CoefficientList[Series[1/((1-2x)(1-5x)(1-7x)(1-8x)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {22, -171, 542, -560}, {1, 22, 313, 3666}, 30] (* Harvey P. Dale, Jan 29 2013 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-5*x)*(1-7*x)*(1-8*x)))); // Bruno Berselli, May 09 2013
(PARI) a(n) = n+=3; (5*8^n-9*7^n+5*5^n-2^n)/90 \\ Charles R Greathouse IV, Oct 03 2016

Crossrefs

Cf. A000079, A000351, A000420, A001018, A016127, A016130, A016131, A016161, A016162,A016177, A016296, A016297, A016311, A019928 - see comments.

Sequence in context: A100789 A028038 A348266 * A028034 A028231 A326277

Adjacent sequences: A025989 A025990 A025991 * A025993 A025994 A025995

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved