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%I #10 Nov 03 2018 18:48:19
%S 1,0,5,4,1,0,21,20,17,16,5,4,1,0,85,84,81,80,69,68,65,64,21,20,17,16,
%T 5,4,1,0,341,340,337,336,325,324,321,320,277,276,273,272,261,260,257,
%U 256,85,84,81,80,69,68,65,64,21,20,17,16,5,4,1,0,1365,1364,1361,1360,1349
%N A divide-and-conquer sequence.
%C Row sums of number triangle A115636. Partial sums of A115638.
%H Antti Karttunen, <a href="/A115637/b115637.txt">Table of n, a(n) for n = 0..1024</a>
%H R. Stephan, <a href="https://arxiv.org/abs/math/0307027">Divide-and-conquer generating functions. I. Elementary sequences</a>, arXiv:math/0307027 [math.CO], 2003.
%F G.f.: (1/(1-x))*Sum_{k>=0} 4^k*x^(2^(k+1)-2)/(1+x^(2^k)); the g.f. G(x) satisfies G(x) - 4(1+x)*x^2*G(x^2) = 1/(1-x^2).
%o (PARI)
%o up_to = 1024;
%o A115633array(n, k) = (((-1)^n)*if(n==k,1, if((k+k+2)==n, -4, if((k+1)==n, -(1+(-1)^k)/2, 0))));
%o A115637list(up_to) = { my(mA115633=matrix(up_to,up_to,n,k,A115633array(n-1,k-1)), mA115636 = matsolve(mA115633,matid(up_to)), v = vector(up_to)); for(n=1,up_to,v[n] = vecsum(mA115636[n,])); (v); };
%o v115637 = A115637list(up_to+1);
%o A115637(n) = v115637[1+n]; \\ _Antti Karttunen_, Nov 02 2018
%Y Cf. A115633, A115636, A115638 (first differences).
%K easy,nonn,look
%O 0,3
%A _Paul Barry_, Jan 27 2006
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