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

4,2

Links

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

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A001333, A131727.

Sequence in context: A138990 A014543 A343676 * A221313 A238832 A192473

Adjacent sequences: A131604 A131605 A131606 * A131608 A131609 A131610

Keyword

nonn,base

Author

Paul Curtz, Oct 02 2007

Extensions

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

Status

approved