A159349 Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{0,0} transformation (see link).

1, 1, 1, 4, 11, 24, 56, 129, 300, 698, 1623, 3773, 8771, 20390, 47401, 110194, 256170, 595523, 1384423, 3218393, 7481856, 17393205, 40434296, 93998334, 218519615, 507996473, 1180948523, 2745372238, 6382216141, 14836852470, 34491497366

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Richard Choulet, Curtz-like transformation.

Index entries for linear recurrences with constant coefficients, signature (3,-2,1).

Formula

O.g.f.: (1-2x+2x^3-2x^5+2x^6-2x^7+x^8)/(1-3x+2x^2-x^3). [corrected by Georg Fischer, May 19 2019]

a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n>=9, with a(0)=1, a(1)=1, a(2)=1, a(3)=4, a(4)=11, a(5)=24, a(6)=56, a(7)=129, a(8)=300.

Maple

a(0):=1: a(1):=1:a(2):=1: a(3):=4:a(4):=11:a(5):=24:a(6):=56:a(7):=129:a(8):=300: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[{1, 1, 1, 4, 11, 24}, LinearRecurrence[{3, -2, 1}, {56, 129, 300}, 95]] (* G. C. Greubel, Jun 16 2018 *)

Prog

(PARI) m=50; v=concat([56, 129, 300], vector(m-3)); for(n=4, m, v[n]= 3*v[n-1] -2*v[n-2] +v[n-3]); concat([1, 1, 1, 4, 11, 24], v) \\ G. C. Greubel, Jun 16 2018
(Magma) I:=[56, 129, 300]; [1, 1, 1, 4, 11, 24] 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 16 2018

Crossrefs

Cf. A137531, A159347, A159348.

Sequence in context: A364282 A159350 A159348 * A349569 A349570 A192597

Adjacent sequences: A159346 A159347 A159348 * A159350 A159351 A159352

Keyword

easy,nonn

Author

Richard Choulet, Apr 11 2009

Status

approved