A249994 Expansion of 1/((1-2*x)*(1+3*x)*(1-4*x)).
1, 3, 19, 63, 307, 1095, 4843, 18111, 76483, 294327, 1213147, 4747119, 19308979, 76282599, 308006731, 1223430687, 4919576995, 19600876311, 78636062395, 313847102415, 1257480899731, 5023648225863, 20113423216939, 80397210315903, 321758305696387, 1286524863041655
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,10,-24).
Crossrefs
Programs
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Magma
[(5*2^(2*n+3) -7*2^(n+1) +(-1)^n*3^(n+2))/35: n in [0..40]]; // G. C. Greubel, Oct 10 2022
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Mathematica
LinearRecurrence[{3,10,-24}, {1,3,19}, 41] (* G. C. Greubel, Oct 10 2022 *) -
PARI
Vec(1/((2*x-1)*(3*x+1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Dec 29 2014
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SageMath
[(5*2^(2*n+3) -7*2^(n+1) +(-1)^n*3^(n+2))/35 for n in range(41)] # G. C. Greubel, Oct 10 2022
Formula
G.f.: 1/((1-2*x)*(1+3*x)*(1-4*x)).
a(n) = (5*2^(2*n+3) - 7*2^(n+1) + (-1)^n*3^(n+2))/35. - Colin Barker, Dec 29 2014
a(n) = 3*a(n-1) + 10*a(n-2) - 24*a(n-3). - Colin Barker, Dec 29 2014
E.g.f.: (1/35)*(9*exp(-3*x) - 14*exp(2*x) + 40*exp(4*x)). - G. C. Greubel, Oct 10 2022