A163478 - OEIS

%I #8 Nov 02 2022 07:46:36

%S 0,1,6,10,30,51,68,84,164,245,330,414,482,551,616,680,1000,1321,1646,

%T 1970,2310,2651,2988,3324,3596,3869,4146,4422,4682,4943,5200,5456,

%U 6736,8017,9302,10586,11886,13187,14484,15780,17140,18501,19866,21230

%N Row sums of A163233 and A163235 divided by 3.

%H Michael De Vlieger, <a href="/A163478/b163478.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.

%F a(n) = A163242(n)/3.

%t 1/3*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, 43}, {j, i, 0, -1}]] (* _Michael De Vlieger_, Nov 01 2022 *)

%Y Cf. A163233, A163235, A163242.

%K nonn

%O 0,3

%A _Antti Karttunen_, Jul 29 2009