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A115714
Periodic {1,-1,-3,0,1,-5,1,0,-3,-1,1,-4}.
2
1, -1, -3, 0, 1, -5, 1, 0, -3, -1, 1, -4, 1, -1, -3, 0, 1, -5, 1, 0, -3, -1, 1, -4, 1, -1, -3, 0, 1, -5, 1, 0, -3, -1, 1, -4, 1, -1, -3, 0, 1, -5, 1, 0, -3, -1, 1, -4, 1, -1, -3, 0, 1, -5, 1, 0, -3, -1, 1, -4, 1, -1, -3, 0, 1, -5, 1, 0, -3, -1, 1, -4
OFFSET
0,3
COMMENTS
Diagonal sums of number triangle A115713.
FORMULA
G.f.: (1 - 3*x^2 + 4*x^3 + 3*x^4 + 4*x^5)/(1 + x + x^2 - x^4 - x^5 - x^6).
a(n) = Sum_{k=0..floor(n/2)} A115713(n-k, k).
MATHEMATICA
LinearRecurrence[{-1, -1, 0, 1, 1, 1}, {1, -1, -3, 0, 1, -5}, 80] (* G. C. Greubel, Nov 23 2021 *)
PROG
(Sage)
def A115714_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-3*x^2+4*x^3+3*x^4+4*x^5)/(1+x+x^2-x^4-x^5-x^6) ).list()
A115714_list(80) # G. C. Greubel, Nov 23 2021
CROSSREFS
Cf. A115713.
Sequence in context: A333852 A179552 A119879 * A346242 A020768 A246182
KEYWORD
easy,sign
AUTHOR
Paul Barry, Jan 29 2006
STATUS
approved