A131727 -id:A131727 - cp's OEIS frontend

A131711 Period 12: repeat 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1.

0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1, 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1, 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1, 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1

Offset: 0

Paul Curtz, Sep 14 2007

Final digits of Pell numbers. First differences: 1, 1, 3, -3, 7, -9, 9, -1, -3, 3 -7, -1, 1 (cf. A131707).

Can be though of as 2 interlocking sequences, each of the form a(n) = a(n - 1) - a(n - 2) + a(n - 3) - a(n - 4) + a(n - 5).

Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1,0,1,0,-1,0,1).

PadRight[{},120,{0,1,2,5,2,9,0,9,8,5,8,1}] (* Harvey P. Dale, Dec 29 2014 *)

[0,1,2,5,2,9,0,9,8,5,8,1][n%12+1] \\ Charles R Greathouse IV, Jun 02 2011

G.f.: (x^8+8x^7+4x^6+5x^4+4x^2+2x+1)x/((1-x) (1+x) (x^2+x+1) (x^2-x+1) (x^4-x^2+1)). a(n) = |A131201(n)| = A000129(n) mod 10 = A000129(n)-10*A131727(n). [From R. J. Mathar, Sep 20 2008]

a(n) = 25/6 -4*cos(Pi*n/6)/sqrt(3) -sqrt(3)*sin(Pi*n/6) -5*cos(Pi*n/3)/3 -5*cos(2*Pi*n/3)/3 +4*cos(5*Pi*n/6)/sqrt(3) +sqrt(3)*sin(5*Pi*n/6) -5*(-1)^n/6. - R. J. Mathar, Oct 08 2011

A131607 Pell companion numbers A001333 without last digit.

Original entry on oeis.org

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

Paul Curtz, Oct 02 2007

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

Cf. A001333, A131727.

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

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

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)

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

cp's OEIS Frontend

A131711 Period 12: repeat 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1.

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