OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..650
Index entries for linear recurrences with constant coefficients, signature (32, 32, 32, -528).
FORMULA
G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
From G. C. Greubel, Apr 28 2019: (Start)
a(n) = 32*(a(n-1) + a(n-2) + a(n-3)) - 528*a(n-4).
G.f.: (1+x)*(1-x^4)/(1 - 33*x + 560*x^4 - 528*x^5). (End)
MATHEMATICA
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(528*t^4-32*t^3-32*t^2 - 32*t+1), {t, 0, 20}], t] (* or *)
LinearRecurrence[{32, 32, 32, -528}, {1, 34, 1122, 37026, 1221297}, 20] (* G. C. Greubel, Dec 11 2016; simplified by Georg Fischer, Apr 08 2019 *)
coxG[{4, 528, -32}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 06 2018 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-33*x+560*x^4-528*x^5)) \\ G. C. Greubel, Dec 11 2016, modified Apr 28 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-33*x+560*x^4-528*x^5) )); // G. C. Greubel, Apr 28 2019
(Sage) ((1+x)*(1-x^4)/(1-33*x+560*x^4-528*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[34, 1122, 37026, 1221297];; for n in [5..20] do a[n]:=32*(a[n-1]+ a[n-2]+a[n-3]) -528*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved