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A151747 Except for boundary cases (n <= 3, j = 0, 1, 2^i-1), satisfies a(n) = a(2^i+j) = 2 a(j) + a(j+1), where n = 2^i + j, 0 <= j < 2^i . 6
0, 1, 3, 5, 8, 9, 11, 17, 21, 15, 11, 18, 25, 29, 39, 54, 53, 27, 11, 18, 25, 29, 39, 55, 57, 41, 40, 61, 79, 97, 132, 160, 129, 51, 11, 18, 25, 29, 39, 55, 57, 41, 40, 61, 79, 97, 132, 161, 133, 65, 40, 61, 79, 97, 133, 167, 155, 122, 141, 201, 255, 326, 424, 448, 305, 99, 11, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The boundary cases are covered by the following formulas:

a(n) = 2n-1 if n<=3.

a(n) = 1+(3*i+1)*2^(i-2) if j=0.

a(n) = 3+ 3*2^(i-1) if j= 1.

a(n) = 2*a(j)+a(j+1)-1 if j=2^i-1.

LINKS

Table of n, a(n) for n=0..67.

David Applegate, The movie version [See A151725, variant]

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata

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

EXAMPLE

If written as a triangle:

.0,

.1,

.3, 5,

.8, 9, 11, 17,

.21, 15, 11, 18, 25, 29, 39, 54,

.53, 27, 11, 18, 25, 29, 39, 55, 57, 41, 40, 61, 79, 97, 132, 160,

.129, 51, 11, 18, 25, 29, 39, 55, 57, 41, 40, 61, 79, 97, 132, 161, 133, 65, 40, 61, 79, 97, 133, 167, 155, 122, 141, 201, 255, 326, 424, 448,

.305, 99, 11, 18, 25, 29, 39, 55, 57, 41, 40, 61, 79, 97, 132, 161, 133, 65, 40, 61, 79, 97, 133, 167, 155, 122, 141, 201, 255, 326, 424, 449, 309, 113, 40, 61, 79, 97, 133, 167, 155, 122, 141, 201, 255, 326, 425, 455, 331, 170, 141, 201, 255, 327, 433, 489, 432, 385, 483, 657, 836, 1076, 1296, 1200,

.705, 195, 11, 18, 25, 29, 39, 55, 57, 41, 40, 61, 79, 97, 132, 161, 133, 65, 40, 61, 79, 97, 133, 167, 155, 122, 141, 201, 255, 326, 424, 449, 309, 113, 40, 61, 79, 97, 133, 167, 155, 122, 141, 201, 255, 326, 425, 455, 331, 170, 141, 201, 255, 327, 433, 489, 432, 385, 483, 657, 836, 1076, 1296, 1201, 709, 209, 40, 61, 79, 97, 133, 167, 155, 122, 141, 201, 255, 326, 425, 455, 331, 170, 141, 201, 255, 327, 433, 489, 432, 385, 483, 657, 836, 1076, 1297, 1207, 731, 266, 141, 201, 255, 327, 433, 489, 432, 385, 483, 657, 836, 1077, 1305, 1241, 832, 481, 483, 657, 837, 1087, 1355, 1410, 1249, 1253, 1623, ...

then the rows (omitting the first two terms of each row) converge to A151748.

MAPLE

A151747 := proc(n) option remember; local i, j;

if (n <= 0) then

  0;

elif (n <= 3) then

  2*n-1;

else

   i := floor(log(n)/log(2));

   j := n - 2^i;

   if (j = 0) then (3*i+1)*2^(i-2)+1;

   elif (j = 1) then 3*2^(i-1)+3;

   elif (j = 2^i-1) then 2*procname(j)+procname(j+1)-1;

   else 2*procname(j)+procname(j+1);

   end if;

end if;

end proc;

CROSSREFS

Cf. A151725, A151726, A151735, A151748, A139250, A170879.

The first column gives A170881.

Sequence in context: A261786 A124401 A292526 * A088597 A080640 A189164

Adjacent sequences:  A151744 A151745 A151746 * A151748 A151749 A151750

KEYWORD

nonn,tabf

AUTHOR

David Applegate, Jun 16 2009

STATUS

approved

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Last modified February 18 20:32 EST 2018. Contains 299330 sequences. (Running on oeis4.)