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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 (list; graph; refs; listen; history; text; internal format)
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(n-1) + 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^(#b-i)-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: A046962 A022486 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

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Last modified July 2 04:07 EDT 2015. Contains 259128 sequences.