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A224924
Sum_{i=0..n} Sum_{j=0..n} (i AND j), where AND is the binary logical AND operator.
4
0, 1, 3, 12, 16, 33, 63, 112, 120, 153, 211, 300, 408, 553, 735, 960, 976, 1041, 1155, 1324, 1536, 1809, 2143, 2544, 2952, 3433, 3987, 4620, 5320, 6105, 6975, 7936, 7968, 8097, 8323, 8652, 9072, 9601, 10239, 10992, 11800, 12729, 13779, 14956, 16248, 17673, 19231, 20928
OFFSET
0,3
COMMENTS
For n>0, a(2^n)-A000217(2^n)=a(2^n-1)-A000217(2^n-1) [See links]. - R. J. Cano, Aug 21 2013
LINKS
Enrique Pérez Herrero, Table of n, a(n) for n = 0..1000
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, pp. 42-43.
FORMULA
a(2^n) = a(2^n - 1) + 2^n.
a(n) -a(n-1) = 2*A222423(n) -n. - R. J. Mathar, Aug 22 2013
MAPLE
read("transforms") :
A224924 := proc(n)
local a, i, j ;
a := 0 ;
for i from 0 to n do
for j from 0 to n do
a := a+ANDnos(i, j) ;
end do:
end do:
a ;
end proc: # R. J. Mathar, Aug 22 2013
MATHEMATICA
a[n_] := Sum[BitAnd[i, j], {i, 0, n}, {j, 0, n}];
Table[a[n], {n, 0, 20}]
(* Enrique Pérez Herrero, May 30 2015 *)
PROG
(Python)
for n in range(99):
s = 0
for i in range(n+1):
for j in range(n+1):
s += i & j
print(s, end=', ')
(PARI) a(n)=sum(i=0, n, sum(j=0, n, bitand(i, j))); \\ R. J. Cano, Aug 21 2013
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Alex Ratushnyak, Apr 19 2013
STATUS
approved