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

0,4

Links

Table of n, a(n) for n=0..84.

Formula

a(2^n) = 1.

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

Example

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

Prog

(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

Crossrefs

Cf. A028310, A052955.

Sequence in context: A277314 A120562 A178692 * A033666 A281511 A381856

Adjacent sequences: A364141 A364142 A364143 * A364145 A364146 A364147

Keyword

nonn,base

Author

Jeffrey Shallit, Jul 10 2023

Extensions

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

Status

approved