A159342 Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{0,1} transform (see link).
2, 3, 6, 16, 39, 89, 207, 480, 1116, 2595, 6033, 14025, 32604, 75795, 176202, 409620, 952251, 2213715, 5146263, 11963610, 27812019, 64655100, 150304872, 349416435, 812294661, 1888355985, 4389895068, 10205267895, 23724369534, 55152467880
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Richard Choulet, Curtz-like transformation.
- Index entries for linear recurrences with constant coefficients, signature (3,-2,1).
Programs
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Magma
I:=[207, 480, 1116]; [2, 3, 6, 16, 39, 89] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) +Self(n-3): 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:a(5):=89:a(6):=207:a(7):=480:a(8):=1116:for n from 6 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i),i=0..31);
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Mathematica
Join[{2, 3, 6, 16, 39, 89}, LinearRecurrence[{3, -2, 1}, {207, 480, 1116}, 50]] (* G. C. Greubel, Jun 17 2018 *) -
PARI
m=50; v=concat([207, 480, 1116], vector(m-3)); for(n=4, m, v[n] = 3*v[n-1] -2*v[n-2] +v[n-3]); concat([2, 3, 6, 16, 39, 89], v) \\ G. C. Greubel, Jun 17 2018
Formula
O.g.f.: ((1-x)^2/(1-3*x+2*x^2-x^3))*(1-x^2+x^4+x^6)+((1-x+x^2)/(1-3*x+2*x^2-x^3)).
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 9, with a(0)=2, a(1)=3, a(2)=6, a(3)=16, a(4)=39, a(5)=89, a(6)=207, a(7)=480, a(8)=1116.