

A274715


Exponent in the power of 2 that equals the denominator in the coefficients of the g.f. described by A274714.


2



0, 0, 0, 0, 0, 1, 0, 1, 0, 3, 0, 3, 2, 4, 0, 4, 3, 7, 1, 7, 6, 8, 4, 8, 7, 10, 6, 10, 9, 11, 5, 11, 10, 15, 9, 15, 14, 16, 12, 16, 15, 18, 14, 18, 17, 19, 14, 19, 18, 22, 17, 22, 21, 23, 19, 23, 22, 25, 21, 25, 24, 26, 19, 26, 25, 31, 24, 31, 30, 32, 28, 32, 31, 34, 30, 34, 33, 35, 30, 35, 34, 38, 33, 38, 37, 39, 35, 39, 38, 41, 37, 41, 40, 42, 36, 42, 41, 46, 40, 46, 45, 47, 43, 47, 46, 49, 45, 49, 48, 50, 45, 50, 49, 53, 48, 53, 52, 54, 50, 54, 53, 56, 52, 56, 55, 57, 49, 57, 56, 63, 55, 63, 62, 64, 60, 64, 63, 66, 62, 66, 65, 67, 62, 67, 66, 70, 65, 70, 69, 71
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OFFSET

1,10


COMMENTS

G.f. of A274714 satisfies: F(x) = x + F(x)^2  R(A(x)^2) + sqrt(F(x)^2  R(F(x)^2)), where R(F(x)) = x, and F(x) = Sum_{n>=1} a(n)*x^n / 2^a(n).


LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..1040


FORMULA

a(2^n) = 2^(n1)  n for n>=1.
a(4*n) = A005187(n1) for n>=1.
a(4*n2) = A005187(n1) for n>=1.
a(4*n3)  a(4*n1) = A001511(n) for n>5, where 2*n/2^A001511(n) is odd.


PROG

(PARI) {a(n) = my(A=x+x^2, R=x); for(i=1, n,
R = serreverse(A + x^2*O(x^n));
A = x + A^2  subst(R, x, A^2) + sqrt(A^2  subst(R, x, A^2)) );
valuation(denominator(polcoeff(A, n)), 2)}
for(n=1, 80, print1(a(n), ", "))


CROSSREFS

Cf. A274714, A274716, A274717.
Sequence in context: A221166 A004604 A246924 * A324180 A271860 A219428
Adjacent sequences: A274712 A274713 A274714 * A274716 A274717 A274718


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Jul 08 2016


STATUS

approved



