A109300 - OEIS

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A109300

a(n) = number of positive integers whose rote height in gammas is n.

1, 1, 7, 999999991 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	COMMENTS	a(n) is the sequence of first differences of A050924. Conversely, A050924 is the sequence of partial sums of a(n). This can be seen as follows. Let P(0) c P(1) c ... c P(n) c ... be an increasing sequence of sets of partial functions that is defined by the recursion: P(0) = {the empty function}, P(n+1) = {partial functions: P(n) -> P(n)}. Then \|P(n)\| = A050924(n+1) = number of positive integers of rote height at most n, hence \|P(n)\| - \|P(n-1)\| = a(n) = number of positive integers of rote height exactly n.
	FORMULA	`a(n) is defined by the recursion a(n+1) = (b(n) + 1)^b(n) - b(n), where a(0) = 1 and b(n) = Sum_[0, n] a(i).`
	EXAMPLE	`Table of Rotes and Primal Functions for Positive Integers of Rote Height 2` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` o-o ` ` o-o ` ` ` o-o ` o-o o-o ` ` o-o o-o ` ` ` o-o o-o ` ` o-o o-o o-o \| ` ` ` \| ` ` ` ` \| ` ` \| ` \| ` ` ` \| ` \| ` ` ` ` \| ` \| ` ` ` \| ` \| ` \| ` o-o ` o-o ` ` o-o o-o ` o---o ` ` o-o ` o-o ` o-o o---o ` ` o-o ` o---o ` \| ` ` \| ` ` ` \| ` \| ` ` \| ` ` ` ` \| ` ` \| ` ` \| ` \| ` ` ` ` \| ` ` \| ` ` ` O ` ` O ` ` ` O===O ` ` O ` ` ` ` O=====O ` ` O===O ` ` ` ` O=====O ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 2:1 ` 1:2 ` ` 1:1 2:1 ` 2:2 ` ` ` 1:2 2:1 ` ` 1:1 2:2 ` ` ` 1:2 2:2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 3 ` ` 4 ` ` ` 6 ` ` ` ` 9 ` ` ` ` 12` ` ` ` ` 18` ` ` ` ` ` 36` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
	CROSSREFS	`Cf. A007097, A050924, A061396, A062504, A062537, A062860.` `Cf. A109301, A106177, A108352, A108371, A111791 to A111800.` `Sequence in context: A172771 A116257 A075984 * A124272 A128820 A067485` `Adjacent sequences: A109297 A109298 A109299 * A109301 A109302 A109303`
	KEYWORD	`nonn`
	AUTHOR	`Jon Awbrey (jawbrey(AT)att.net), Jul 04 2005, revised Sep 06 2005`

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Last modified February 14 08:06 EST 2012. Contains 205604 sequences.