A274715 Exponent in the power of 2 that equals the denominator in the coefficients of the g.f. described by A274714.

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

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^(n-1) - n for n>=1.

a(4*n) = A005187(n-1) for n>=1.

a(4*n-2) = A005187(n-1) for n>=1.

a(4*n-3) - a(4*n-1) = 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