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

0,3

Comments

Fixed points are in A000225.

Links

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

Formula

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

Example

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.

Maple

with(combinat, permute): P:=proc(q) local a, b, c, j, k, n, t, v; v:=[];
for n from 0 to q do a:=convert(n, base, 2); b:=permute(a); t:=0; for k from 1 to nops(b) do
c:=0; for j from 1 to nops(a) do c:=2*c+b[k][-j]; od; t:=t+c; od; v:=[op(v), t];
od; op(v) end: P(56);
# second Maple program:
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 *)

Crossrefs

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

Sequence in context: A214825 A230017 A134346 * A049772 A119470 A060368

Adjacent sequences: A378956 A378957 A378958 * A378960 A378961 A378962

Keyword

nonn,base

Author

Paolo P. Lava, Dec 12 2024

Status

approved