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%I #22 Jun 25 2022 17:07:08
%S 1,4,13,16,43,52,61,64,145,172,199,208,235,244,253,256,499,580,661,
%T 688,769,796,823,832,913,940,967,976,1003,1012,1021,1024,1753,1996,
%U 2239,2320,2563,2644,2725,2752,2995,3076,3157,3184,3265,3292,3319,3328,3571,3652,3733,3760,3841,3868,3895
%N a(n) = r*a(ceiling(n/2))+s*a(floor(n/2)) with a(1)=1 and (r,s)=(3,1).
%C 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
%C 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
%H K.-N. Chang and S.-C. Tsai, <a href="http://dx.doi.org/10.1016/S0020-0190(00)00076-4">Exact solution of a minimal recurrence</a>, Inform. Process. Lett. 75 (2000), 61-64.
%o (PARI) a(n) = if (n==1, 1, 3*a(ceil(n/2)) + a(floor(n/2))); \\ _Michel Marcus_, Mar 24 2016
%Y 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.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Feb 16 2016
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