OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,-1).
FORMULA
a(n) = 2*a(n-8) - a(n-16).
G.f.: x*(1 + x + x^2)*(1 + x^2 + x^4)*(1 + x^4 + x^8)/(1 - x^8)^2. - G. C. Greubel, Oct 26 2019
MAPLE
seq(coeff(series(x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2, x, n+1), x, n), n = 0 .. 90); # G. C. Greubel, Oct 26 2019
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1}, {0, 1, 1, 2, 1, 3, 2, 3, 1, 5, 4, 7, 3, 8, 5, 7}, 90] (* Harvey P. Dale, May 10 2012 *)
CoefficientList[Series[x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2, {x, 0, 90}], x]
PROG
(PARI) my(x='x+O('x^90)); concat([0], Vec(x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2)) \\ G. C. Greubel, Oct 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 90); [0] cat Coefficients(R!( x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2 )); // G. C. Greubel, Oct 26 2019
(Sage)
def A026730_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1+x+x^2)*(1+x^2+x^4)*(1+x^4+x^8)/(1-x^8)^2 ).list()
A026730_list(90) # G. C. Greubel, Oct 26 2019
(GAP) a:=[0, 1, 1, 2, 1, 3, 2, 3, 1, 5, 4, 7, 3, 8, 5, 7];; for n in [17..90] do a[n]:=2*a[n-8]-a[n-16]; od; a; # G. C. Greubel, Oct 26 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
J. Carl Bellinger (carlb(AT)ctron.com)
EXTENSIONS
Shorter description and more terms from David W. Wilson
STATUS
approved