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A115269 Row sums of correlation triangle for floor((n+4)/4).

%I A115269 #25 Sep 21 2018 09:20:34
%S A115269 1,2,4,6,11,16,24,32,46,60,80,100,130,160,200,240,295,350,420,490,581,
%T A115269 672,784,896,1036,1176,1344,1512,1716,1920,2160,2400,2685,2970,3300,
%U A115269 3630,4015,4400,4840,5280,5786,6292,6864,7436,8086,8736,9464,10192,11011,11830
%N A115269 Row sums of correlation triangle for floor((n+4)/4).
%C A115269 Row sums of number triangle A115268.
%H A115269 Harvey P. Dale, <a href="/A115269/b115269.txt">Table of n, a(n) for n = 0..1000</a>
%H A115269 Hamzeh Mujahed, Benedek Nagy, <a href="https://dx.doi.org/10.7546/CRABS.2018.05.13">Hyper-Wiener Index on Rows of Unit Cells of the BCC Grid</a>, Comptes rendus de l’Académie bulgare des Sciences, Tome 71, No 5, 2018, 675-684. See p. 8.
%H A115269 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,3,-4,0,4,-3,2,0,-2,1).
%F A115269 G.f.: (1+x+x^2+x^3)^2/((1-x^4)^4*(1-x^2));
%F A115269 a(n) = Sum_{k=0..n} Sum_{j=0..n} [j<=k]*floor((k-j+4)/4)*[j<=n-k]*floor((n-k-j+4)/4).
%F A115269 a(n) = 2*a(n-1) -2*a(n-3) +3*a(n-4) -4*a(n-5) +4*a(n-7) -3*a(n-8) +2*a(n-9) -2*a(n-11) +a(n-12).
%F A115269 G.f.: -1 / ( (x^2+1)^2*(1+x)^3*(x-1)^5 ). - _R. J. Mathar_, Nov 28 2014
%F A115269 a(n) = (2*(n^4+24*n^3+197*n^2+636*n)+3*(431+(2*n^2+24*n+65)*(-1)^n)+24*((n+7)*(-1)^((2*n-1+(-1)^n)/4)-(n+5)*(-1)^((6*n-1+(-1)^n)/4)))/1536. - _Luce ETIENNE_, Mar 03 2015
%t A115269 CoefficientList[Series[(1+x+x^2+x^3)^2/((1-x^4)^4(1-x^2)), {x,0,50}], x] (* _Harvey P. Dale_, Aug 20 2011 *)
%o A115269 (PARI) a(n) = sum(k=0, n, sum(j=0, n, (j<=k)*((k-j+4)\4)*(j<=n-k)*((n-k-j+4)\4))); \\ _Michel Marcus_, Apr 09 2015
%K A115269 easy,nonn
%O A115269 0,2
%A A115269 _Paul Barry_, Jan 18 2006
%E A115269 More terms from _Michel Marcus_, Apr 09 2015