A115637 A divide-and-conquer sequence.

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

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