A171069 G.f. -x*(x-1)*(1+x)/(1-x-12*x^2-x^3+x^4).

0, 1, 1, 12, 25, 169, 480, 2521, 8425, 38988, 142129, 615889, 2352000, 9845809, 38543569, 158429388, 628446025, 2558296441, 10219534560, 41389108489, 165953373625, 670283913612, 2692893971041, 10860865199521, 43679923392000

Offset: 0

Author

R. J. Mathar, at the request of R. K. Guy, Sep 03 2010

Keywords

• nonn
• easy

Comments

The member k=12 of a family of sequences starting 0,1,1,k with recurrence a(n) = a(n-1)+k*a(n-2)+a(n-3)-a(n-4).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Hugh Williams, R. K. Guy, Some fourth-order linear divisibility sequences, Intl. J. Number Theory vol. 7 (5) (2011) 1255-1277
• Index entries for linear recurrences with constant coefficients, signature (1,12,1,-1).

Crossrefs

Cf. A116201 (k=1), A105309 (k=2), A152090 (k=3), A007598 (k=4), A005178 (k=5), A003757 (k=6).

Programs

Magma

I:=[0, 1, 1, 12]; [n le 4 select I[n] else Self(n-1) + 12*Self(n-2) + Self(n-3) - Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 19 2012

Mathematica

CoefficientList[Series[-x*(x - 1)*(1 + x)/(1 - x - 12*x^2 - x^3 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)
LinearRecurrence[{1,12,1,-1},{0,1,1,12},30] (* Harvey P. Dale, Nov 04 2024 *)

Formula

a(n)= +a(n-1) +12*a(n-2) +a(n-3) -a(n-4).