A159350 Transform of A056594 by the T_{0,0} transformation (see link).
1, 1, 1, 4, 11, 24, 54, 127, 297, 689, 1600, 3721, 8652, 20112, 46753, 108689, 252673, 587392, 1365519, 3174448, 7379698, 17155715, 39882197, 92714861, 215535904, 501060185, 1164823608, 2707886360, 6295072049, 14634267033, 34020543361
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..2700
- 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:=[1,1,1,4,11]; [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 15 2018
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Maple
a(0):=1: a(1):=1: a(2):=1: a(3):=4: a(4):=11: 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}, {1,1,1,4,11}, 50] (* G. C. Greubel, Jun 15 2018 *) -
PARI
x='x+O('x^50); Vec((1-x)^2/((1-3*x+2*x^2-x^3)*(1+x^2))) \\ G. C. Greubel, Jun 15 2018
Formula
O.g.f.: (1-z)^2/((1-3*z+2*z^2-z^3)*(1+z^2)).
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)=1, a(1)=1, a(2)=1, a(3)=4, a(4)=11.