id:A135017 - OEIS Search Results

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a(n) = number of strings of length n that can be obtained by starting with abc and repeatedly doubling any substring in place, and then discarding any string that contains two successive equal letters.

+0
5

0, 0, 1, 0, 2, 1, 3, 5, 7, 15, 20, 48, 60, 156, 205, 489, 761, 1572, 2796, 5357, 10174, 19021, 37272, 69375, 137759, 258444, 513696, 976890, 1934900, 3727164, 7358675, 14316861, 28217028, 55288907, 108942267, 214462953, 422973649 (list; graph; listen)

	OFFSET	`1,5`
	COMMENT	`These strings may be regarded as the "primitive" strings among those enumerated by A135473.` `Equals the inverse binomial transform of A135473.`
	LINKS	`Index entries for doubling substrings`
	FORMULA	`Empirically, grows like 2^n.`
	EXAMPLE	`n=3: abc` `n=4: -` `n=5: ababc, abcbc` `n=6: abcabc` `n=7: abababc, ababcbc, abcbcbc`
	CROSSREFS	`Cf. A135473.` `Adjacent sequences: A135014 A135015 A135016 this_sequence A135018 A135019 A135020` `Sequence in context: A006769 A075643 A076074 this_sequence A070168 A021828 A094341`
	KEYWORD	`nonn`
	AUTHOR	`David Applegate and njas, Feb 12 2008`
	EXTENSIONS	`Extended to 37 terms by David Applegate, Feb 16 2008`

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Last modified January 8 02:43 EST 2009. Contains 152824 sequences.

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