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

0,1

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).

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.

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);

Mathematica

Join[{2, 3, 6, 16, 39, 89}, LinearRecurrence[{3, -2, 1}, {207, 480, 1116}, 50]] (* G. C. Greubel, Jun 17 2018 *)

Prog

(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
(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

Crossrefs

Cf. A135364, A159340, A159341.

Sequence in context: A369560 A159343 A159341 * A089872 A006402 A284417

Adjacent sequences: A159339 A159340 A159341 * A159343 A159344 A159345

Keyword

easy,nonn

Author

Richard Choulet, Apr 11 2009

Status

approved