A024346 Expansion of 1/((1-x)*(1-6*x)*(1-9*x)*(1-11*x)).
1, 27, 484, 7266, 98959, 1269177, 15642586, 187539120, 2204181925, 25529358855, 292445725936, 3321943348542, 37489352241979, 420930326166741, 4707254688375814, 52473555698990412, 583456285162491601
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (27,-245,813,-594).
Programs
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Magma
R
:=PowerSeriesRing(Integers(), 25); Coefficients(R!(1/((1-x)*(1-6*x)*(1-9*x)*(1-11*x)))); // Vincenzo Librandi, Jul 16 2013 -
Magma
I:=[1,27,484,7266]; [n le 4 select I[n] else 27*Self(n-1)-245*Self(n-2)+813*Self(n-3)-594*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 16 2013
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Mathematica
CoefficientList[Series[1/((1-x)(1-6x)(1-9x)(1-11x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 16 2013 *) LinearRecurrence[{27,-245,813,-594},{1,27,484,7266},20] (* Harvey P. Dale, Oct 13 2016 *) -
PARI
a(n) = (12*11^(n+3) - 25*9^(n+3) + 16*6^(n+3) - 3)/1200; \\ Joerg Arndt, Aug 13 2013
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Sage
[(4*11^(n+3) -75*9^(n+2) +32*6^(n+2) -1)/400 for n in (0..20)] # G. C. Greubel, Jan 30 2022
Formula
a(n) = 27*a(n-1) - 245*a(n-2) + 813*a(n-3) - 594*a(n-4) for n > 3; a(0)=1, a(1)=27, a(2)=484, a(3)=7266. - Vincenzo Librandi, Jul 16 2013
a(n) = (12*11^(n+3) - 25*9^(n+3) + 16*6^(n+3) - 3)/1200. - Yahia Kahloune, Aug 13 2013
E.g.f.: (1/400)*(-exp(x) + 1152*exp(6*x) - 6075*exp(9*x) + 5324*exp(11*x)). - G. C. Greubel, Jan 30 2022