A269589 Number of triples 0 <= i, j, k < n such that bitwise AND of i, j, k is 0.

1, 7, 25, 49, 109, 175, 265, 343, 559, 763, 1015, 1225, 1573, 1855, 2161, 2401, 3217, 3913, 4705, 5341, 6325, 7105, 7933, 8575, 9943, 11011, 12127, 12985, 14197, 15127, 16081, 16807, 19975, 22519, 25255, 27391, 30511, 32935, 35455, 37387

Offset: 1

Author

Peter Karpov, Mar 01 2016

Keywords

• nonn

Comments

Start with A = [[[1]]], iteratively replace every element Aijk with Aijk * [[[1, 1], [1, 1]], [[1, 1], [1, 0]]]. a(n) is the sum of the resulting array inside the cubic region i, j, k < n. - Peter Karpov, Mar 01 2016

a(n) is a lower bound on A268239. - Peter Karpov, Mar 01 2016

Links

• Peter Karpov, InvMem, Item 21

Crossrefs

Cf. A268524.

Programs

Mathematica

a[n_] := If[Mod[n, 2] == 0, 7 a[n/2], 4 a[(n + 1)/2] + 3 a[(n - 1)/2] - 6 * 2^DigitCount[n, 2, 0]]; a[1] := 1;
Table[a[i], {i, 1, 40}]

Formula

a(1) = 1, a(2*n) = 7*a(n), a(2*n+1) = 4*a(n+1) + 3*a(n) - 6*A080100(2*n+1).