A370627 a(n) = 2^(n - 1)*((-1)^(n + 1) + 7*2^n)/3 = 2^(n - 1)*A062092(n).
1, 5, 18, 76, 296, 1200, 4768, 19136, 76416, 305920, 1223168, 4893696, 19572736, 78295040, 313171968, 1252704256, 5010784256, 20043202560, 80172679168, 320690978816, 1282763390976, 5131054612480, 20524216352768, 82096869605376, 328387470032896, 1313549896908800, 5254199554080768
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (2,8).
Programs
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Mathematica
LinearRecurrence[{2, 8}, {1, 5}, 27] (* Amiram Eldar, Jul 03 2024 *) -
PARI
a(n) = 2^(n-1)*((-1)^(n+1) + 7*2^n)/3 \\ Thomas Scheuerle, Jul 03 2024
Formula
Binomial transform of A133125.
G.f.: (1 + 3*x)/(1 - 2*x - 8*x^2).
E.g.f.: (1/3)*exp(x)*(3*exp(3*x) + sinh(3*x)).
a(n) = 2*a(n-1) + 8*a(n-2), for n > 1.
a(n) = 4*a(n-1) + (-2)^n, for n > 0.
a(n) = (a(n+2) - 2*a(n+1))/8.
From Thomas Scheuerle, Jul 03 2024: (Start)
a(n) = 2^(n - 1)*((-1)^(n + 1) + 7*2^n)/3.
a(n) = A003683(n) + 4^n.
Binomial transform: A108982.