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A105348 An indicator sequence for the Jacobsthal numbers. 9
1, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of solutions to the Diophantine equation 2*x^2 - (9*n+1)*x + 9*n^2 = 1 where valid solutions are restricted to powers of 4. - Hieronymus Fischer, May 17 2007

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..87381

FORMULA

G.f.: Sum_{k>=0} x^A001045(k).

a(n) = 1 + floor(log_2(3n+1)) - ceiling(log_2(3n-1)) = floor(log_2(3n+1)) - floor(log_2(3n-2)) for n >= 1. Also true: a(n) = 1 + A130249(n) - A130250(n) = A130253(n) - A130250(n) = A130250(n+1) - A130250(n) for n >= 0. - Hieronymus Fischer, May 17 2007

EXAMPLE

a(1)=2 since J(1)=J(2)=1.

PROG

(PARI)

A147612aux(n, i) = if(!(n%2), n, A147612aux((n+i)/2, -i));

A147612(n) = 0^(A147612aux(n, 1)*A147612aux(n, -1));

A105348(n) = if(1==n, 2, A147612(n)); \\ Antti Karttunen, Nov 02 2018

CROSSREFS

For partial sums see A130253. Cf. A130249, A130250, A147612.

Sequence in context: A237996 A203951 A323591 * A016406 A129182 A116857

Adjacent sequences:  A105345 A105346 A105347 * A105349 A105350 A105351

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 01 2005

STATUS

approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)