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A258438
Sum_{i=1..n} Sum_{j=1..n} (i OR j), where OR is the binary logical OR operator.
1
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
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
KEYWORD
nonn,base
AUTHOR
STATUS
approved