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A159339
Transform of A056594 by the T_{1,0} transformation (see link).
1
1, 2, 4, 11, 27, 61, 140, 327, 762, 1770, 4113, 9563, 22233, 51684, 120149, 279314, 649328, 1509503, 3509167, 8157825, 18964644, 44087447, 102490878, 238262386, 553892849, 1287644651, 2993410641, 6958835472, 16177329785, 37607729050
OFFSET
0,2
FORMULA
O.g.f.: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1/(1+z^2))+(z/(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)=1, a(1)=2, a(2)=4, a(3)=11, a(4)=27.
MAPLE
a(0):=1: a(1):=2:a(2):=4: a(3):=11:a(4):=27: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);
MATHEMATICA
LinearRecurrence[{3, -3, 4, -2, 1}, {1, 2, 4, 11, 27}, 50] (* G. C. Greubel, Jun 25 2018 *)
PROG
(PARI) z='z+O('z^50); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1/(1+z^2))+(z/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 25 2018
(Magma) I:=[1, 2, 4, 11, 27]; [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 25 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Apr 11 2009
STATUS
approved