A151747 - OEIS

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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 .

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; 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+(3i+1)2^(i-2) if j=0.` `a(n) = 3+ 32^(i-1) if j= 1.` `a(n) = 2a(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` `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` `2n-1;` `else` `i := floor(log(n)/log(2));` `j := n - 2^i;` `if (j = 0) then (3i+1)2^(i-2)+1;` `elif (j = 1) then 32^(i-1)+3;` `elif (j = 2^i-1) then 2procname(j)+procname(j+1)-1;` `else 2procname(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: A034784 A190280 A124401 * A088597 A080640 A189164` `Adjacent sequences: A151744 A151745 A151746 * A151748 A151749 A151750`
	KEYWORD	`nonn,tabf`
	AUTHOR	`David Applegate (david(AT)research.att.com), Jun 16 2009`

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Last modified February 17 00:09 EST 2012. Contains 205978 sequences.