OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..643
Index entries for linear recurrences with constant coefficients, signature (35, 35, -630).
FORMULA
G.f.: (t^3 + 2*t^2 + 2*t + 1)/(630*t^3 - 35*t^2 - 35*t + 1).
G.f.: (1+x)*(1-x^3)/(1 - 36*x + 665*x^3 - 630*x^4). - G. C. Greubel, Apr 26 2019
a(n) = 35*a(n-1)+35*a(n-2)-630*a(n-3). - Wesley Ivan Hurt, May 05 2021
MATHEMATICA
CoefficientList[Series[(t^3+2*t^2+2*t+1)/(630*t^3-35*t^2-35*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{35, 35, -630}, {1, 37, 1332}, 20] (* G. C. Greubel, Oct 24 2018 *)
coxG[{3, 630, -35}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)
PROG
(PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(630*t^3-35*t^2-35*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 +2*t^2+2*t+1)/(630*t^3-35*t^2-35*t+1))); // G. C. Greubel, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1-36*x+665*x^3-630*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019
(GAP) a:=[37, 1332, 47286];; for n in [4..20] do a[n]:=35*a[n-1]+ 35*a[n-2]-630*a[n-3]; od; Concatenation([1], a); # G. C. Greubel, Apr 26 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved