OFFSET
1,19
COMMENTS
Same as A025828 with zeros prepended. - Joerg Arndt, Nov 04 2014
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..999
Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,0,1,-1,0,-1,-1,0,0,1).
FORMULA
G.f.: x^13/((1-x^3)*(1-x^4)*(1-x^6)). - Tani Akinari, Nov 04 2014
From Robert Israel, Nov 04 2014: (Start)
a(n) = a(n-3) + a(n-4) + a(n-6) - a(n-7) - a(n-9) - a(n-10) + a(n-13) for n >= 14.
a(6*n) = (2*n^2 - 8*n + 7 + (-1)^n)/8, n >= 1.
a(6*n+1) = a(6*n+4) = a(6*n+5) = (2*n^2 - 1 + (-1)^n)/8.
a(6*n+2) = a(6*n+3) = (2*n^2 - 4*n + 1 - (-1)^n)/8.
(End)
MATHEMATICA
LinearRecurrence[{0, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, 100] (* Harvey P. Dale, Sep 04 2017 *)
PROG
(Sage)
def A024165_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( x^13/((1-x^3)*(1-x^4)*(1-x^6)) ).list()
a=A024165_list(100); a[1:] # G. C. Greubel, Jul 03 2021
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 100);
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] cat Coefficients(R!( x^13/((1-x^3)*(1-x^4)*(1-x^6)) )); // G. C. Greubel, Jul 03 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved