

A116528


Starting a(0)=0, a(1)=1, recursively a(2n)=a(n), a(2n+1)= 2*a(n) + a(n+1).


2



0, 1, 1, 3, 1, 5, 3, 7, 1, 7, 5, 13, 3, 13, 7, 15, 1, 9, 7, 19, 5, 23, 13, 29, 3, 19, 13, 33, 7, 29, 15, 31, 1, 11, 9, 25, 7, 33, 19, 43, 5, 33, 23, 59, 13, 55, 29, 61, 3, 25, 19, 51, 13, 59, 33, 73, 7, 43, 29, 73, 15, 61, 31, 63, 1, 13
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OFFSET

0,4


COMMENTS

Equals row 2 of the array in A178239, an infinite set of sequences of the form a(n) = a(2n), a(2n+1) = r*a(n) + a(n+1).  Gary W. Adamson, May 23 2010


LINKS

Table of n, a(n) for n=0..65.
H. Harborth, Number of Odd Binomial Coefficients, Proc. Amer. Math. Soc. 62, 1922, 1977.
Eric Weisstein's World of Mathematics, StolarskyHarborth Constant


FORMULA

Given an infinite lower triangular matrix M with (1, 1, 2, 0, 0, 0,...) in every column, shifted down twice for columns k>1; Lim_{n>inf} M^n = A116528, the leftshifted vector considered as a sequence with offset 1.  Gary W. Adamson, May 05 2010


MAPLE

A116528 := proc(n)
option remember;
if n <= 1 then
n;
elif type(n, 'even') then
procname(n/2) ;
else
2* procname((n1)/2)+procname((n+1)/2) ;
end if;
end proc:
seq(A116528(n), n=0..80) ; # R. J. Mathar, Nov 16 2011


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 + 1)/2] a = Table[b[n], {n, 1, 50}]


CROSSREFS

Cf. A006046.
Sequence in context: A161398 A204455 A161820 * A081431 A053641 A161825
Adjacent sequences: A116525 A116526 A116527 * A116529 A116530 A116531


KEYWORD

nonn,easy


AUTHOR

Roger L. Bagula, Mar 15 2006


STATUS

approved



