id:A124756 - OEIS Search Results

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Inverse binomial sum of compositions in standard order.

+0
3

0, 1, 2, 0, 3, 1, -1, 0, 4, 2, 0, 1, -2, -2, 1, 0, 5, 3, 1, 2, -1, -1, 2, 1, -3, -4, -1, -3, 2, 3, -1, 0, 6, 4, 2, 3, 0, 0, 3, 2, -2, -3, 0, -2, 3, 4, 0, 1, -4, -6, -3, -6, 0, 0, -4, -4, 3, 6, 2, 6, -2, -4, 1, 0, 7, 5, 3, 4, 1, 1, 4, 3, -1, -2, 1, -1, 4, 5, 1, 2, -3, -5, -2, -5, 1, 1, -3, -3, 4, 7, 3, 7, -1, -3, 2, 1, -5, -8, -5, -9, -2 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`The standard order of compositions is given by A066099.` `This is the final term of the inverse binomial transform of the composition.`
	FORMULA	`For a composition b(1),...,b(k), a(n) = Sum_{i=1}^k (-1)^{i-1} C(k-1,i-1) b(i).`
	EXAMPLE	`Composition number 11 is 2,1,1; 12-21+1*1 = 1, so a(11) = 1.` `The table starts:` `0` `1` `2 0` `3 1 -1 0`
	CROSSREFS	`Cf. A066099, A124754, A124755, A011782 (row lengths), A001477 (row sums).` `Sequence in context: A074650 A144955 A002187 this_sequence A113504 A124754 A047983` `Adjacent sequences: A124753 A124754 A124755 this_sequence A124757 A124758 A124759`
	KEYWORD	`easy,sign,tabf`
	AUTHOR	`Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 06 2006`

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.

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