

A151920


a(n) = (Sum_{i=1..n+1} 3^wt(i))/3, where wt() = A000120().


14



1, 2, 5, 6, 9, 12, 21, 22, 25, 28, 37, 40, 49, 58, 85, 86, 89, 92, 101, 104, 113, 122, 149, 152, 161, 170, 197, 206, 233, 260, 341, 342, 345, 348, 357, 360, 369, 378, 405, 408, 417, 426, 453, 462, 489, 516, 597, 600, 609, 618, 645, 654, 681, 708, 789, 798, 825, 852, 933, 960
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OFFSET

0,2


COMMENTS

Partial sums of A147610 (but with offset changed to 0).
It appears that the first bisection gives the positive terms of A147562.  Omar E. Pol, Mar 07 2015


LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..10000
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to cellular automata


FORMULA

a(n) = (A147562(n+2)  1)/4 = (A151917(n+2)  1)/2.  Omar E. Pol, Mar 13 2011
a(n) = (A130665(n+1)  1)/3.  Omar E. Pol, Mar 07 2015
a(n) = a(n1) + 3^A000120(n+1))/3.  David A. Corneth, Mar 21 2015


EXAMPLE

n=3: (3^1+3^1+3^2+3^1)/3 = 18/3 = 6.
n=18: the binary expansion of 18+1 is 10011, i.e., 19 = 2^4 + 2^1 + 2^0.
The exponents of these powers of 2 (4, 1 and 0) reoccur as exponents in the powers of 4: a(19) = 3^0 * [(4^4  1) / 3 + 1] + 3^1 * [(4^1  1) / 3 + 1] + 3^2 * [(4^0  1)/3 + 1] = 1 * 86 + 3 * 2 + 9 * 1 = 101.  David A. Corneth, Mar 21 2015


MATHEMATICA

t = Nest[Join[#, # + 1] &, {0}, 14]; Table[Sum[3^t[[i + 1]], {i, 1, n}]/3, {n, 60}] (* Michael De Vlieger, Mar 21 2015 *)


PROG

(PARI) a(n) = sum(i=1, n+1, 3^hammingweight(i))/3; \\ Michel Marcus, Mar 07 2015
(PARI) a(n)={b=binary(n+1); t=#b; e=1; sum(i=1, #b, e+=(b[i]==1); (b[i]==1)*3^e*((4^(#bi)1)/3+1))} \\ David A. Corneth, Mar 21 2015


CROSSREFS

Cf. A130665, A147562, A147610, A153000, A160410, A160414.  Omar E. Pol, Nov 12 2009
Cf. A139250, A151917, A152998.  Omar E. Pol, Mar 13 2011
Sequence in context: A022486 A267700 A161910 * A160714 A256644 A219764
Adjacent sequences: A151917 A151918 A151919 * A151921 A151922 A151923


KEYWORD

nonn,easy,look


AUTHOR

N. J. A. Sloane, Aug 05 2009, Aug 06 2009


STATUS

approved



