A159347 Transform of the finite sequence (1, 0, -1) by the T_{0,0} transformation.

1, 1, 1, 4, 10, 23, 53, 123, 286, 665, 1546, 3594, 8355, 19423, 45153, 104968, 244021, 567280, 1318766, 3065759, 7127025, 16568323, 38516678, 89540413, 208156206, 483904470, 1124941411, 2615171499, 6079536145, 14133206848, 32855719753

Offset: 0

Author

Richard Choulet, Apr 11 2009

Keywords

• easy
• nonn

Comments

Without the first two 1's: A137531.

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).

Crossrefs

Cf. A137531.

Programs

Magma

I:=[1,4,10]; [1,1] 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

Maple

a(0):=1: a(1):=1:a(2):=1: a(3):=4:a(4):=10:for n from 2 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}, LinearRecurrence[{3,-2,1}, {1,4,10}, 50]] (* G. C. Greubel, Jun 16 2018 *)

PARI

m=50; v=concat([1,4,10], vector(m-3)); for(n=4, m, v[n] = 3*v[n-1] -2*v[n-2] +v[n-3] ); concat([1,1], v) \\ G. C. Greubel, Jun 16 2018

Formula

O.g.f.: f(z) = ((1-z)^2/(1 - 3*z + 2*z^2 - z^3))*(1-z^2).

a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) for n >= 5, with a(0)=1, a(1)=1, a(2)=1, a(3)=4, a(4)=10.

a(n) = A137531(n-2).