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A021194
Expansion of 1/((1-x)(1-2x)(1-6x)(1-9x)).
1
1, 18, 223, 2388, 23809, 228246, 2138131, 19746936, 180745477, 1644848634, 14912475799, 134865314844, 1217706037705, 10982863580382, 98986827702427, 891727782261312, 8030628038119693, 72306120329946690
OFFSET
0,2
FORMULA
a(0)=1, a(1)=18, a(2)=223, a(3)=2388, a(n)=18*a(n-1)-101*a(n-2)+ 192*a(n-3)- 108*a(n-4) [From Harvey P. Dale, Jul 18 2011]
a(n)=(5*9^(n+3) - 14*6^(n+3) +30*2^(n+3) - 21)/840. [Yahia Kahloune, Jun 26 2013]
a(0)=1, a(1)=18; for n>1, a(n) = 15*a(n-1) -54* a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013
MATHEMATICA
LinearRecurrence[{18, -101, 192, -108}, {1, 18, 223, 2388}, 30] (* or *) CoefficientList[ Series[1 / ((1 - x) (1 - 2 x) (1 - 6 x) (1 - 9 x)), {x, 0, 30}], x] (* Harvey P. Dale, Jul 18 2011 *)
PROG
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-6*x)*(1-9*x)))); /* or */ I:=[1, 18, 223, 2388]; [n le 4 select I[n] else 18*Self(n-1)-101*Self(n-2)+192*Self(n-3)-108*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 08 2013
CROSSREFS
Sequence in context: A021224 A017997 A018911 * A155049 A155073 A153709
KEYWORD
nonn,easy
AUTHOR
STATUS
approved