A159338 Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{1,0} transformation (see link).
1, 2, 4, 11, 27, 61, 140, 327, 761, 1769, 4112, 9559, 22222, 51660, 120095, 279187, 649031, 1508814, 3507567, 8154104, 18955992, 44067335, 102444125, 238153697, 553640176, 1287057259, 2992045122, 6955661024, 16169950087, 37590573335
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:=[140, 327, 761]; [1, 2, 4, 11, 27, 61] 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 25 2018
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Maple
a(0):=1: a(1):=2:a(2):=4: a(3):=11:a(4):=27:a(5):=61:a(6):=140:a(7):=327:a(8):=761: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[{1, 2, 4, 11, 27, 61}, LinearRecurrence[{3, -2, 1}, {140, 327, 761}, 45]] (* G. C. Greubel, Jun 25 2018 *) -
PARI
z='z+O('z^50); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4-z^6)+(z/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 25 2018
Formula
O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4-z^6)+(z/(1-3*z+2*z^2-z^3)).
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 9, with a(0)=1, a(1)=2, a(2)=4, a(3)=11, a(4)=27, a(5)=61, a(6)=140, a(7)=327, a(8)=761.