A131607 Pell companion numbers A001333 without last digit.

1, 4, 9, 23, 57, 139, 336, 811, 1960, 4732, 11424, 27580, 66585, 160752, 388089, 936931, 2261953, 5460839, 13183632, 31828103, 76839840, 185507784, 447855408, 1081218600, 2610292609, 6301803820, 15213900249, 36729604319, 88673108889, 214075822099, 516824753088

Offset: 4

Author

Paul Curtz, Oct 02 2007

Keywords

• nonn
• base

Links

• Andrew Howroyd, Table of n, a(n) for n = 4..1000

Crossrefs

Cf. A001333, A131727.

Programs

Mathematica

Table[Floor[(((1 - Sqrt[2])^n + (1 + Sqrt[2])^n)/2)/10], {n, 4, 29}] (* Metin Sariyar, Jan 03 2020 *)

PARI

a(n)={polcoef((1 - x) / (1 - 2*x - x^2) + O(x*x^n), n)\10} \\ Andrew Howroyd, Jan 02 2020

Formula

a(n) = floor(A001333(n) / 10). - Andrew Howroyd, Jan 02 2020

Conjectures from Colin Barker, Jan 03 2020: (Start)

G.f.: x^4*(1 + x - 2*x^2 + x^3 + x^4) / ((1 - x)*(1 + x^2)*(1 - 2*x - x^2)*(1 - x^2 + x^4)).

a(n) = 3*a(n-1) - a(n-2) - a(n-3) - a(n-6) + 3*a(n-7) - a(n-8) - a(n-9) for n>12.

(End)

Extensions

Offset changed and terms a(24) and beyond from Andrew Howroyd, Jan 02 2020