A125104 - OEIS

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A125104

Triangle read by rows counting compositions (ordered partitions) by minimal part size.

1, 1, 1, 1, 0, 3, 1, 0, 1, 6, 1, 0, 0, 2, 13, 1, 0, 0, 1, 3, 27, 1, 0, 0, 0, 2, 5, 56, 1, 0, 0, 0, 1, 2, 9, 115, 1, 0, 0, 0, 0, 2, 3, 15, 235, 1, 0, 0, 0, 0, 1, 2, 5, 25, 478, 1, 0, 0, 0, 0, 0, 2, 2, 8, 42, 969, 1, 0, 0, 0, 0, 0, 1, 2, 3, 12, 70, 1959, 1, 0, 0, 0, 0, 0, 0, 2, 2, 5, 18, 116, 3952, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 8, 27, 192, 7959, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 11, 41, 317, 16007 (list; table; graph; refs; listen; history; internal format)

	OFFSET	`0,6`
	COMMENTS	`The diagonals of this array can be generated from Table A099238 as follows: A000079 - A000045 = 1 2 4 8 16 32...-0 1 1 2 3 5...= 1 1 3 6 13 27 ... A099036 A000045 - A000930 A000930 - A003269 A003269 - A003520 etc.`
	EXAMPLE	`Row 4 of the array is (1 0 1 6) because there are six compositions with minimum part of size one: 1111 31 13 211 121 112, one of size two: 22, none of size three and 1 of size four: 4.` `Triangle (after 45 degree anticlockwise rotation) begins:` `1 1 3 6 13 27 56 115 235 478 969 1959 3952 7959` `.1 0 1 2 3 5 9 15 25 42 70 116 192` `..1 0 0 1 2 2 3 5 8 12 18 27` `...1 0 0 0 1 2 2 2 3 5 8` `....1 0 0 0 0 1 2 2 2 2` `.....1 0 0 0 0 0 1 2 2` `......1 0 0 0 0 0 0 1` `.......1 0 0 0 0 0 0` `........1 0 0 0 0 0`
	CROSSREFS	`Cf. A000079 A000045 A000930 A003269 A003520 A099036 A099238.` `Cf. A105147.` `Sequence in context: A081719 A121314 A119271 * A098157 A165253 A059045` `Adjacent sequences: A125101 A125102 A125103 * A125105 A125106 A125107`
	KEYWORD	`easy,nonn,tabl`
	AUTHOR	`Alford Arnold (Alford1940(AT)aol.com), Nov 28 2006, corrected Nov 28 2006`
	EXTENSIONS	`Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 21 2006` `More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 10 2007`

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Last modified February 16 10:32 EST 2012. Contains 205904 sequences.