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

Author

Enrique Pérez Herrero, May 30 2015

Keywords

• nonn
• base

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.

Crossrefs

Cf. A224924.

Programs

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}]

PARI

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

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