OFFSET
0,2
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -3).
FORMULA
G.f.: (t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(3*t^12 - 2*t^11 - 2*t^10 - 2*t^9 - 2*t^8 - 2*t^7 - 2*t^6 - 2*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t + 1).
G.f.: (1+x)*(1-x^12)/(1 -3*x +5*x^12 -3*x^13). - G. C. Greubel, Apr 26 2019
a(n) = -3*a(n-12) + 2*Sum_{k=1..11} a(n-k). - Wesley Ivan Hurt, May 06 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^12)/(1 -3*x +5*x^12 -3*x^13), {x, 0, 30}], x ] (* Vincenzo Librandi, Apr 29 2014 *)(* modified by G. C. Greubel, Apr 26 2019 *)
coxG[{12, 3, -2, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 09 2018 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1+x)*(1-x^12)/(1-3*x+5*x^12-3*x^13)) \\ G. C. Greubel, Apr 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^12)/(1-3*x+5*x^12-3*x^13) )); // G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^12)/(1-3*x+5*x^12-3*x^13)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved