A213786 a(n) = Sum_{1<=i<j<=n} b(i)*b(j), where b(k) = A020985(k).

0, 0, 1, -1, 0, 2, -1, 1, 4, 8, 13, 7, 2, -2, 1, -3, 0, 4, 9, 3, 8, 14, 7, 13, 6, 0, -5, -1, 4, 10, 3, 9, 16, 24, 33, 23, 32, 42, 31, 41, 52, 64, 77, 63, 50, 38, 49, 37, 26, 16, 7, 15, 6, -2, 5, -3, 4, 12, 21, 11, 2, -6, 1, -7, 0, 8, 17, 7, 16, 26, 15, 25, 36

Offset

0,6

Comments

Suggested by A190173.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Maple

b:= proc(n) option remember; local r;
      `if`(n=0, 1, `if`(irem(n, 2, 'r')=0, b(r), b(r)*(-1)^r))
    end:
s:= proc(j) option remember; `if`(j<2, 0, s(j-1)+b(j-1)) end:
a:= proc(n) option remember; `if`(n<2, 0, a(n-1)+b(n)*s(n)) end:
seq(a(n), n=0..100);  # Alois P. Heinz, Jun 23 2012

Mathematica

b[0] = 1; b[1] = 1; b[n_?EvenQ] := b[n] = b[n/2]; b[n_?OddQ] := b[n] = (-1)^((n-1)/2)*b[(n-1)/2]; a[n_] := Sum[b[i]*b[j], {i, 1, n-1}, {j, i+1, n}]; Table[a[n], {n, 0, 72}] (* Jean-François Alcover, Nov 27 2014 *)

Prog

(Python)
def A213786(n): return sum((-1 if (i&(i>>1)).bit_count()&1 else 1)*sum(-1 if (j&(j>>1)).bit_count()&1 else 1 for j in range(i+1, n+1)) for i in range(1, n+1)) # Chai Wah Wu, Feb 12 2023

Crossrefs

Cf. A020985, A190173.

Sequence in context: A277081 A111569 A371926 * A055130 A051292 A094424

Adjacent sequences: A213783 A213784 A213785 * A213787 A213788 A213789

Keyword

sign

Author

N. J. A. Sloane, Jun 20 2012

Status

approved