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 A115637 A divide-and-conquer sequence. 3
 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, 5, 4, 1, 0, 341, 340, 337, 336, 325, 324, 321, 320, 277, 276, 273, 272, 261, 260, 257, 256, 85, 84, 81, 80, 69, 68, 65, 64, 21, 20, 17, 16, 5, 4, 1, 0, 1365, 1364, 1361, 1360, 1349 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums of number triangle A115636. Partial sums of A115638. LINKS Antti Karttunen, Table of n, a(n) for n = 0..1024 R. Stephan, Divide-and-conquer generating functions. I. Elementary sequences, arXiv:math/0307027 [math.CO], 2003. FORMULA 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). PROG (PARI) up_to = 1024; A115633array(n, k) = (((-1)^n)*if(n==k, 1, if((k+k+2)==n, -4, if((k+1)==n, -(1+(-1)^k)/2, 0)))); 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); }; v115637 = A115637list(up_to+1); A115637(n) = v115637[1+n]; \\ Antti Karttunen, Nov 02 2018 CROSSREFS Cf. A115633, A115636, A115638 (first differences). Sequence in context: A133842 A199453 A245699 * A124602 A320060 A132707 Adjacent sequences:  A115634 A115635 A115636 * A115638 A115639 A115640 KEYWORD easy,nonn,look AUTHOR Paul Barry, Jan 27 2006 STATUS approved

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Last modified July 27 07:23 EDT 2021. Contains 346304 sequences. (Running on oeis4.)