A187732 Expansion of x/(x^4 - 13x^3 + 36x^2 - 13x + 1).

0, 1, 13, 133, 1274, 11942, 111098, 1030791, 9554727, 88535307, 820278004, 7599523660, 70405203700, 652259875085, 6042764572481, 55982252063633, 518638725390318, 4804846035350514, 44513730857759982, 412390365056271763, 3820524794586339931, 35394642842712164887, 327908025365023678952

Offset: 0

Author

N. J. A. Sloane, Mar 13 2011

Keywords

• nonn
• easy

Comments

This g.f. arose in a discussion with R. K. Guy about divisibility sequences.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (13,-36,13,-1).

Programs

Mathematica

CoefficientList[Series[x / (x^4 - 13 x^3 + 36 x^2 - 13 x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)
LinearRecurrence[{13,-36,13,-1},{0,1,13,133},30] (* Harvey P. Dale, Mar 10 2015 *)

Maxima

makelist(coeff(taylor(x/(x^4-13*x^3+36*x^2-13*x+1), x, 0, n), x, n), n, 0, 22);  /* Bruno Berselli, Jun 05 2011 */

PARI

a=[0,1,13,133];for(i=1,99,a=concat(a, 13*a[#a]-36*a[#a-1]+13*a[#a-2]-a[#a-3]));a \\ Charles R Greathouse IV, Jun 05 2011

Formula

a(0)=0, a(1)=1, a(2)=13, a(3)=133, a(n)=13*a(n-1)-36*a(n-2)+ 13*a(n-3)- a(n-4). - Harvey P. Dale, Mar 10 2015