A048644 Differences between partial sums of Gray code (A048641) and triangular numbers (A000217).
0, 0, 1, 0, 2, 4, 3, 0, 4, 8, 13, 16, 14, 12, 7, 0, 8, 16, 25, 32, 42, 52, 59, 64, 60, 56, 53, 48, 38, 28, 15, 0, 16, 32, 49, 64, 82, 100, 115, 128, 148, 168, 189, 208, 222, 236, 247, 256, 248, 240, 233, 224, 218, 212, 203, 192, 172, 152, 133, 112, 86, 60, 31, 0, 32, 64
Offset: 0
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..10000
- Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 40.
Programs
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Mathematica
{0}~Join~MapIndexed[#1 - PolygonalNumber[First[#2]] &, Accumulate[Array[BitXor[#, Floor[#/2]] &, 65]]] (* Michael De Vlieger, Oct 29 2022 *) -
PARI
a(n) = sum(k=0, n, bitxor(k, k>>1)) - n*(n+1)/2; \\ Michel Marcus, Oct 02 2015
Formula
a(n) = sum(XORnos(j, floor(j/2)), j=0..n)-((n^2+n)/2).
Extensions
Corrected by Don Reble, May 01 2006
Comments