A085351 Expansion of (1-3*x)/((1-4*x)*(1-5*x)).
1, 6, 34, 186, 994, 5226, 27154, 139866, 715714, 3644106, 18482674, 93461946, 471504034, 2374297386, 11938595794, 59961414426, 300880813954, 1508699037066, 7560675054514, 37872094749306, 189635351653474
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (9,-20).
Programs
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Mathematica
CoefficientList[Series[(1-3x)/((1-4x)(1-5x)),{x,0,20}],x] (* or *) LinearRecurrence[{9,-20},{1,6},30] (* Harvey P. Dale, Jan 07 2022 *) -
PARI
Vec((1 - 3*x) / ((1 - 4*x)*(1 - 5*x)) + O(x^25)) \\ Colin Barker, Jun 25 2020
Formula
G.f.: (1-3*x)/((1-4*x)*(1-5*x)).
a(n) = 2*5^n - 4^n.
a(n) = 9*a(n-1) - 20*a(n-2) for n>1. - Colin Barker, Jun 25 2020
Comments