A378959 Sum, in base 10, of the permutations of the digits of n, written in base 2.

0, 1, 3, 3, 7, 14, 14, 7, 15, 45, 45, 45, 45, 45, 45, 15, 31, 124, 124, 186, 124, 186, 186, 124, 124, 186, 186, 124, 186, 124, 124, 31, 63, 315, 315, 630, 315, 630, 630, 630, 315, 630, 630, 630, 630, 630, 630, 315, 315, 630, 630, 630, 630, 630, 630, 315, 630

Offset: 0

Author

Paolo P. Lava, Dec 12 2024

Keywords

• nonn
• base

Comments

Fixed points are in A000225.

Examples

			a(5) = 14 because 5 in base 2 is 101 and the permutations of the digits are 101, 110, 011 that correspond to 5, 6, 3 and 5 + 6 + 3 = 14.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A000120, A000225, A003817, A090706, A134346.

Programs

Maple

a:= proc(n) local k, l;
      l:= convert(n, base, 2); k:= nops(l);
      binomial(k-1, add(i, i=l)-1)*(2^k-1)
    end:
seq(a(n), n=0..56);  # Alois P. Heinz, Dec 12 2024

Mathematica

A378959[n_] := (2^# - 1)*Binomial[# - 1, DigitCount[n, 2, 0]] & [BitLength[n]];
Array[A378959, 100, 0] (* Paolo Xausa, Jan 29 2025 *)

Formula

a(n) = A003817(n) * A090706(n). - Alois P. Heinz, Dec 12 2024