A258438 Sum_{i=1..n} Sum_{j=1..n} (i OR j), where OR is the binary logical OR operator.

0, 1, 9, 24, 64, 117, 189, 280, 456, 657, 889, 1152, 1464, 1813, 2205, 2640, 3376, 4161, 5001, 5896, 6864, 7893, 8989, 10152, 11448, 12817, 14265, 15792, 17416, 19125, 20925, 22816, 25824, 28929, 32137, 35448, 38880, 42421, 46077, 49848, 53800

Offset

0,3

Links

Giovanni Resta, Table of n, a(n) for n = 0..10000

Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 42.

Formula

a(2^k) = (3*8^k+5*4^k)/4-2^k. - Giovanni Resta, May 30 2015

a(2^k-1) = 2^(k-2) * (4 - 7*2^k + 3*4^k). - Enrique Pérez Herrero, Jun 10 2015

a(n) = n^3 + n^2 - A224924(n). - Robert Israel, Jun 11 2015

Maple

A[0]:= 0:
for n from 1 to 100 do
  A[n]:= A[n-1] + n + 2*add(Bits[Or](i, n), i=1..n-1)
od:
seq(A[i], i=0..100); # Robert Israel, Jun 11 2015

Mathematica

a[n_] := Sum[BitOr[i, j], {i, 1, n}, {j, 1, n}]; Table[a[n], {n, 0, 40}]

Prog

(PARI) a(n) = sum(i=1, n, sum(j=1, n, bitor(i, j))); \\ Michel Marcus, May 31 2015

Crossrefs

Cf. A224924.

Sequence in context: A079770 A079771 A297225 * A038626 A195970 A223372

Adjacent sequences: A258435 A258436 A258437 * A258439 A258440 A258441

Keyword

nonn,base

Author

Enrique Pérez Herrero, May 30 2015

Status

approved