A105348 An indicator sequence for the Jacobsthal numbers.

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

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 A370078 A129182

Adjacent sequences: A105345 A105346 A105347 * A105349 A105350 A105351

Keyword

easy,nonn

Author

Paul Barry, Apr 01 2005

Status

approved