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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
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
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 A372332
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 01 2005
STATUS
approved