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%I #16 Apr 03 2016 10:54:58
%S 1,7,25,49,109,175,265,343,559,763,1015,1225,1573,1855,2161,2401,3217,
%T 3913,4705,5341,6325,7105,7933,8575,9943,11011,12127,12985,14197,
%U 15127,16081,16807,19975,22519,25255,27391,30511,32935,35455,37387
%N Number of triples 0 <= i, j, k < n such that bitwise AND of i, j, k is 0.
%C 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
%C a(n) is a lower bound on A268239. - _Peter Karpov_, Mar 01 2016
%H Peter Karpov, <a href="http://inversed.ru/InvMem.htm#InvMem_21">InvMem, Item 21</a>
%F 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).
%t 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;
%t Table[a[i], {i, 1, 40}]
%Y Cf. A268524.
%K nonn
%O 1,2
%A _Peter Karpov_, Mar 01 2016
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