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A006583
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a(n) = Sum_{k=1..n-1} (k OR n-k).
(Formerly M4069)
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4
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1, 6, 8, 16, 25, 42, 44, 56, 69, 94, 108, 136, 165, 210, 208, 224, 241, 278, 296, 336, 377, 442, 460, 504, 549, 622, 668, 744, 821, 930, 912, 928, 945, 998, 1016, 1072, 1129, 1226, 1244, 1304
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OFFSET
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2,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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G.f.: 1/(1-x)^2 * sum(k>=0, 2^k*t^2(4t^2+6t+1)/(1+t)^2, t=x^2^k). - Ralf Stephan, Feb 12 2003
a(0)=a(1)=0, a(2n) = 2a(n)+2a(n-1)+5n-4, a(2n+1) = 4a(n)+6n. - Ralf Stephan, Oct 09 2003
a(n) = 2*(Sum_{k=1..floor((n-1)/2)} k OR n-k) + m where m is 0 if n is odd and n/2 otherwise. - Chai Wah Wu, May 07 2023
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MATHEMATICA
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Table[Sum[BitOr[k, n-k], {k, n-1}], {n, 2, 50}] (* Harvey P. Dale, Dec 05 2020 *)
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PROG
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(Python)
def A006583(n): return (sum(k|n-k for k in range(1, n+1>>1))<<1)+(0 if n&1 else n>>1) # Chai Wah Wu, May 07 2023
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CROSSREFS
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Antidiagonal sums of array A003986.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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