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A159341
Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,1} transformation (see link).
2
2, 3, 6, 16, 39, 89, 206, 479, 1114, 2590, 6021, 13997, 32539, 75644, 175851, 408804, 950354, 2209305, 5136011, 11939777, 27756614, 64526299, 150005446, 348720354, 810676469, 1884594145, 4381149851, 10184937732, 23677107639, 55042597304
OFFSET
0,1
FORMULA
O.g.f: f(z) = ((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4) + ((1-z+z^2)/(1-3*z+2*z^2-z^3)).
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 7, with a(0)=2, a(1)=3, a(2)=6, a(3)=16, a(4)=39, a(5)=89, a(6)=206.
MAPLE
a(0):=2: a(1):=3:a(2):=6: a(3):=16:a(4):=39:a(5):=89:a(6):=206:for n from 4 to 31 do a(n+3):=3*a(n+2)-2*a(n+1)+a(n):od:seq(a(i), i=0..31);
MATHEMATICA
Join[{2, 3, 6, 16}, LinearRecurrence[{3, -2, 1}, {39, 89, 206}, 47]] (* G. C. Greubel, Jun 25 2018 *)
PROG
(PARI) z='z+O('z^30); Vec(((1-z)^2/(1-3*z+2*z^2-z^3))*(1-z^2+z^4) + ((1-z+z^2)/(1-3*z+2*z^2-z^3))) \\ G. C. Greubel, Jun 25 2018
(Magma) I:=[39, 89, 206]; [2, 3, 6, 16] cat [n le 3 select I[n] else 3*Self(n-1) - 2*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Jun 25 2018
CROSSREFS
Sequence in context: A159340 A369560 A159343 * A159342 A089872 A006402
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Apr 11 2009
STATUS
approved