

A116529


AntiHarborth alternating chaotic sequence, 2nd type.


6



1, 1, 2, 1, 3, 2, 5, 1, 4, 3, 7, 2, 7, 5, 12, 1, 7, 4, 9, 3, 10, 7, 17, 2, 11, 7, 16, 5, 17, 12, 29, 1, 14, 7, 15, 4, 15, 9, 22, 3, 15, 10, 23, 7, 24, 17, 41, 2, 21, 11, 24, 7, 25, 16, 39, 5, 26, 17, 39, 12, 41, 29, 70, 1, 31, 14, 29, 7, 28, 15
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OFFSET

0,3


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2500
H. Harborth, Number of Odd Binomial Coefficients, Proc. Amer. Math. Soc. 62, 1922, 1977.
Eric Weisstein's World of Mathematics, StolarskyHarborth Constant


FORMULA

From G. C. Greubel, Oct 30 2016: (Start)
a(2*n + 1) = a(n), n>=1.
a(2*n + 2) = 2*a(n) + a(n1), n>=1. (End)
G.f. g(x) satisfies g(x) = 1 + (x^4+2*x^2+x)*g(x^2).  Robert Israel, Nov 13 2017


MAPLE

gg:= 1:
for iter from 1 to 7 do
gg:= convert(series(1+(x^4+2*x^2+x)*eval(gg, x=x^2), x, 2^iter+1), polynom)
od:
seq(coeff(gg, x, n), n=0..2^7); # Robert Israel, Nov 13 2017


MATHEMATICA

b[0] := 0; b[1] := 1; b[n_?EvenQ] := b[n] = b[n/2]; b[n_?OddQ] := b[n] = 2*b[(n  1)/2] + b[(n  3)/2]; a = Table[b[n], {n, 1, 70}]


CROSSREFS

Cf. A116528, A116552, A116553, A116554, A116555.
Sequence in context: A300383 A120250 A280689 * A169747 A269380 A268674
Adjacent sequences: A116526 A116527 A116528 * A116530 A116531 A116532


KEYWORD

nonn,obsc


AUTHOR

Roger L. Bagula, Mar 15 2006


EXTENSIONS

Name changed by G. C. Greubel, Oct 30 2016


STATUS

approved



