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A159912 Partial sums of A159913(k) = 2^bitcount(2k+1)-1 = A038573(2k+1), bitcount=A000120. 5
0, 1, 4, 7, 14, 17, 24, 31, 46, 49, 56, 63, 78, 85, 100, 115, 146, 149, 156, 163, 178, 185, 200, 215, 246, 253, 268, 283, 314, 329, 360, 391, 454, 457, 464, 471, 486, 493, 508, 523, 554, 561, 576, 591, 622, 637, 668, 699, 762, 769, 784, 799, 830, 845, 876, 907 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

More precisely, a(n)=sum(i<n, A159913(i)), since we want the sequence to start with a(0)=0 and not with A159913(0)=1.

a(n) is also the total number of ON cells after n generations in the outward corner version of the Ulam-Warburton cellular automaton of A147562, and a(n) is also the total number of Y-toothpicks after n generations in the outward corner version of the Y-toothpick structure of A160120. - David Applegate and Omar E. Pol, Jan 24 2016

LINKS

Table of n, a(n) for n=0..55.

David Applegate, The movie version

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to cellular automata

Index entries for sequences related to toothpick sequences

FORMULA

a(n) = sum( i=0...n-1, A159913(i)) = sum(i=0..n-1, 2^A000120(i))*2-n

a(n) = n + (A160720(n) - 1)/2 = n + 2*(A266532(n) - 1)/3 = n + 2*A267700(n-1), n >= 1. - Omar E. Pol, Jan 25 2016

MATHEMATICA

Accumulate@ Table[2^(DigitCount[n, 2][[1]] + 1) - 1, {n, 0, 54}] (* Michael De Vlieger, Jan 25 2016 *)

PROG

(PARI) A159912(n)=sum(i=0, n-1, 1<<norml2(binary(i)))*2-n

CROSSREFS

Cf. A000120, A038573, A147562, A159913, A160120, A160720, A266532, A267700.

Sequence in context: A310906 A310907 A310908 * A183060 A310909 A310910

Adjacent sequences:  A159909 A159910 A159911 * A159913 A159914 A159915

KEYWORD

nonn

AUTHOR

M. F. Hasler, May 03 2009

STATUS

approved

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Last modified February 20 06:26 EST 2019. Contains 320332 sequences. (Running on oeis4.)