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A151917 a(0)=0, a(1)=1; for n>=2, a(n) = (2/3)*(Sum_{i=1..n-1} 3^wt(i)) + 1, where wt() = A000120(). 5
0, 1, 3, 5, 11, 13, 19, 25, 43, 45, 51, 57, 75, 81, 99, 117, 171, 173, 179, 185, 203, 209, 227, 245, 299, 305, 323, 341, 395, 413, 467, 521, 683, 685, 691, 697, 715, 721, 739, 757, 811, 817, 835, 853, 907, 925, 979, 1033, 1195, 1201, 1219 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Also, total number of "ON" cells at n-th stage in two of the four wedges of the "Ulam-Warburton" two-dimensional cellular automaton of A147562, but including the central ON cell. It appears that this is very close to A139250, the toothpick sequence. - Omar E. Pol, Feb 22 2015
LINKS
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. 31.
FORMULA
a(n) = A151914(n)/4.
a(n) = A079315(2n)/4.
For n>=2, a(n) = 2*A151920(n-2) + 1.
For n>=1, a(n) = (1 + A147562(n))/2. - Omar E. Pol, Mar 13 2011
a(2^k) = A007583(k), if k >= 0. - Omar E. Pol, Feb 22 2015
EXAMPLE
n=3: (2/3)*(3^1+3^1+3^2+3^1) + 1 = (2/3)*18 + 1 = 13.
MATHEMATICA
Array[(2/3) Sum[3^(Total@ IntegerDigits[i, 2]), {i, # - 1}] + 1 &, 50] (* Michael De Vlieger, Nov 01 2022 *)
PROG
(PARI) a(n) = if (n<2, n, 1 + 2*sum(i=1, n-1, 3^hammingweight(i))/3); \\ Michel Marcus, Feb 22 2015
CROSSREFS
Sequence in context: A059311 A023209 A020609 * A059639 A059263 A066652
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 05 2009, Aug 06 2009
STATUS
approved

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Last modified March 28 21:57 EDT 2024. Contains 371254 sequences. (Running on oeis4.)