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A006582 a(n) = Sum_{k=1..n-1} k XOR n-k.
(Formerly M4053)
3
0, 6, 4, 12, 20, 42, 32, 40, 48, 78, 84, 116, 148, 210, 176, 176, 176, 214, 212, 252, 292, 378, 368, 408, 448, 542, 580, 676, 772, 930, 832, 800, 768, 806, 772, 812, 852, 970, 928, 968, 1008, 1134, 1172, 1300, 1428, 1650, 1584, 1616, 1648, 1782, 1812, 1948 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

REFERENCES

Marc LeBrun, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

R. J. Mathar, Table of n, a(n) for n = 2..1000

M. Le Brun, Email to N. J. A. Sloane, Jul 1991

FORMULA

G.f.: 1/(1-x)^2 * Sum_{k>=0} 2^k * t^3(4t+6)/(1+t)^2, t=x^2^k. - Ralf Stephan, Feb 12 2003

a(0) = a(1) = 0, a(2n) = 2a(n) + 2a(n-1) + 4n - 4, a(2n+1) = 4a(n) + 6n. - Ralf Stephan, Oct 09 2003

MAPLE

A006582 := proc(n)

    add(A003987(k, n-k), k=1..n-1) ;

end proc: # R. J. Mathar, Apr 17 2013

PROG

(PARI) a(n)=if(n<2, 0, if(n%2==0, 2*a(n/2)+2*a(n/2-1)+4*(n/2-1), 4*a((n-1)/2)+6*((n-1)/2)))

(PARI) a(n)=sum(k=1, n-1, bitxor(k, n-k)) \\ Charles R Greathouse IV, Aug 11 2017

CROSSREFS

Antidiagonal sums of array A003987.

Sequence in context: A141270 A040032 A239394 * A263586 A180497 A213038

Adjacent sequences:  A006579 A006580 A006581 * A006583 A006584 A006585

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 25 12:38 EST 2018. Contains 299654 sequences. (Running on oeis4.)