A364144 Number of distinct representations for n in base 2, using digits -1,0,1, whose sum of digits is 0.

1, 1, 1, 2, 1, 2, 2, 3, 1, 3, 2, 4, 2, 4, 3, 4, 1, 3, 3, 5, 2, 6, 4, 6, 2, 5, 4, 7, 3, 6, 4, 5, 1, 3, 3, 6, 3, 7, 5, 8, 2, 7, 6, 10, 4, 10, 6, 8, 2, 6, 5, 9, 4, 10, 7, 10, 3, 8, 6, 10, 4, 8, 5, 6, 1, 3, 3, 6, 3, 8, 6, 9, 3, 8, 7, 13, 5, 12, 8, 11, 2, 8, 7, 13, 6

Offset: 0

Author

Jeffrey Shallit, Jul 10 2023

Keywords

• nonn
• base

Examples

			a(12) = 2, because 12 = 16-4 = 32-16-8+4.
		

Crossrefs

Cf. A028310, A052955.

Programs

PARI

a364144(upto) = {my (a=vector(upto)); for (k=1, 3^floor(3*log(upto)), my (w=digits(k,3), n); w=apply(x->x-1, w); if (w[1] && vecsum(w)==0, my (n=fromdigits(w,b=2)); if (n>0 && n<=#a, a[n]++))); concat(1,a)};
a364144(70) \\ Hugo Pfoertner, Jul 11 2023

Formula

a(2^n) = 1.

a(2^n-1) = A028310(n).

Extensions

a(0)=1 prepended by Alois P. Heinz, Jul 10 2023