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Row sums of A163233 and A163235.
4

%I #5 Nov 02 2022 07:45:56

%S 0,3,18,30,90,153,204,252,492,735,990,1242,1446,1653,1848,2040,3000,

%T 3963,4938,5910,6930,7953,8964,9972,10788,11607,12438,13266,14046,

%U 14829,15600,16368,20208,24051,27906,31758,35658,39561,43452,47340

%N Row sums of A163233 and A163235.

%C It is easily seen that these terms are always divisible by 3.

%H Michael De Vlieger, <a href="/A163242/b163242.txt">Table of n, a(n) for n = 0..1000</a>

%H Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2210.10968">Identities and periodic oscillations of divide-and-conquer recurrences splitting at half</a>, arXiv:2210.10968 [cs.DS], 2022, pp. 42-43.

%t Map[Total, Table[Function[k, FromDigits[#, 2] &@ Apply[Function[{a, b}, Riffle @@ Map[PadLeft[#, Max[Length /@ {a, b}]] &, {a, b}]], Map[IntegerDigits[#, 2] &@ BitXor[#, Floor[#/2]] &, {k, j}] ] ][i - j], {i, 0, 39}, {j, i, 0, -1}]] (* _Michael De Vlieger_, Nov 01 2022 *)

%Y a(n) = 3*A163478(n).

%K nonn

%O 0,2

%A _Antti Karttunen_, Jul 29 2009