A268524 a(n) = r*a(ceiling(n/2))+s*a(floor(n/2)) with a(1)=1 and (r,s)=(3,1).

1, 4, 13, 16, 43, 52, 61, 64, 145, 172, 199, 208, 235, 244, 253, 256, 499, 580, 661, 688, 769, 796, 823, 832, 913, 940, 967, 976, 1003, 1012, 1021, 1024, 1753, 1996, 2239, 2320, 2563, 2644, 2725, 2752, 2995, 3076, 3157, 3184, 3265, 3292, 3319, 3328, 3571, 3652, 3733, 3760, 3841, 3868, 3895

Offset: 1

Author

N. J. A. Sloane, Feb 16 2016

Keywords

• nonn

Comments

Number of triples 0 <= i, j, k < n such that bitwise AND of all pairs (i, j), (j, k), (k, i) is 0. - Peter Karpov, Mar 01 2016

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

Links

• K.-N. Chang and S.-C. Tsai, Exact solution of a minimal recurrence, Inform. Process. Lett. 75 (2000), 61-64.

Crossrefs

Sequences of form a(n) = r*a(ceiling(n/2))+s*a(floor(n/2)) with a(1)=1 and (r,s) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), (1,4), (2,3), (3,2), (4,1): A000027, A006046, A064194, A130665, A073121, A268524, A116520, A268525, A268526, A268527.

Programs

PARI

a(n) = if (n==1, 1, 3*a(ceil(n/2)) + a(floor(n/2))); \\ Michel Marcus, Mar 24 2016