A115714 - OEIS

%I #19 Dec 14 2023 05:33:00

%S 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,

%T 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,

%U 0,-3,-1,1,-4,1,-1,-3,0,1,-5,1,0,-3,-1,1,-4

%N Periodic {1,-1,-3,0,1,-5,1,0,-3,-1,1,-4}.

%C Diagonal sums of number triangle A115713.

%H G. C. Greubel, <a href="/A115714/b115714.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,0,1,1,1)

%F 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).

%F a(n) = Sum_{k=0..floor(n/2)} A115713(n-k, k).

%t LinearRecurrence[{-1,-1,0,1,1,1}, {1,-1,-3,0,1,-5}, 80] (* _G. C. Greubel_, Nov 23 2021 *)

%o (Sage)

%o def A115714_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     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()

%o A115714_list(80) # _G. C. Greubel_, Nov 23 2021

%Y Cf. A115713.

%K easy,sign

%O 0,3

%A _Paul Barry_, Jan 29 2006