A115714 Periodic {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, 1, -1, -3, 0, 1, -5, 1, 0, -3, -1, 1, -4

Offset: 0

Author

Paul Barry, Jan 29 2006

Keywords

• easy
• sign

Comments

Diagonal sums of number triangle A115713.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,-1,0,1,1,1)

Crossrefs

Cf. A115713.

Programs

Mathematica

LinearRecurrence[{-1,-1,0,1,1,1}, {1,-1,-3,0,1,-5}, 80] (* G. C. Greubel, Nov 23 2021 *)

Sage

def A115714_list(prec):
    P. = 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

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).