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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 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, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.] 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 July 23 17:41 EDT 2021. Contains 346259 sequences. (Running on oeis4.)