A274715 - OEIS

%I #6 Jul 08 2016 12:14:15

%S 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,

%T 10,15,9,15,14,16,12,16,15,18,14,18,17,19,14,19,18,22,17,22,21,23,19,

%U 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

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

%C 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).

%H Paul D. Hanna, <a href="/A274715/b274715.txt">Table of n, a(n) for n = 1..1040</a>

%F a(2^n) = 2^(n-1) - n for n>=1.

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

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

%F a(4*n-3) - a(4*n-1) =  A001511(n) for n>5, where 2*n/2^A001511(n) is odd.

%o (PARI) {a(n) = my(A=x+x^2,R=x); for(i=1,n,

%o R = serreverse(A + x^2*O(x^n));

%o A = x + A^2 - subst(R,x,A^2) + sqrt(A^2 - subst(R,x,A^2)) );

%o valuation(denominator(polcoeff(A,n)),2)}

%o for(n=1,80,print1(a(n),", "))

%Y Cf. A274714, A274716, A274717.

%K nonn

%O 1,10

%A _Paul D. Hanna_, Jul 08 2016