A159343 Transform of A056594 by the T_{0,1} transformation (see link).
2, 3, 6, 16, 39, 89, 205, 478, 1113, 2586, 6010, 13973, 32485, 75517, 175554, 408115, 948754, 2205584, 5127359, 11919665, 27709861, 64417610, 149752773, 348132962, 809310950, 1881419697, 4373770153, 10167782017, 23637225442, 54949882443
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..2500
- Richard Choulet, Curtz-like transformation.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,4,-2,1).
Programs
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Magma
I:=[2, 3, 6, 16, 39]; [n le 5 select I[n] else 3*Self(n-1) -3*Self(n-2) +4*Self(n-3) -2*Self(n-4) +Self(n-5): n in [1..50]]; // G. C. Greubel, Jun 17 2018
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Maple
a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=39:for n from 0 to 31 do a(n+5):=3*a(n+4)-3*a(n+3)+4*a(n+2)-2*a(n+1)+a(n):od:seq(a(i),i=0..31);
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Mathematica
LinearRecurrence[{3, -3, 4, -2, 1}, {2, 3, 6, 16, 39}, 50] (* G. C. Greubel, Jun 17 2018 *) -
PARI
m=32; v=concat([2, 3, 6, 16, 39], vector(m-5)); for(n=6, m, v[n] = 3*v[n-1] -3*v[n-2] +4*v[n-3] -2*v[n-4] +v[n-5]); v \\ G. C. Greubel, Jun 17 2018
Formula
O.g.f.: ((1-z)^2/(1-3*z+2*z^2-z^3))*(1/(1+z^2))+((1-z+z^2)/(1-3*z+2*z^2-z^3)).
a(n) = 3*a(n-1) - 3*a(n-2) + 4*a(n-3) - 2*a(n-4) + a(n-5) for n>=5, with a(0)=2, a(1)=3, a(2)=6, a(3)=16, a(4)=39.