A214246 - OEIS

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A214246

Number A(n,k) of compositions of n where differences between neighboring parts are in {-k,0,k}; square array A(n,k), n>=0, k>=0, read by antidiagonals.

1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 1, 1, 2, 2, 6, 2, 1, 1, 2, 2, 5, 11, 4, 1, 1, 2, 2, 3, 5, 17, 2, 1, 1, 2, 2, 3, 4, 10, 29, 4, 1, 1, 2, 2, 3, 2, 7, 10, 47, 3, 1, 1, 2, 2, 3, 2, 6, 8, 21, 78, 4, 1, 1, 2, 2, 3, 2, 4, 5, 9, 22, 130, 2 (list; table; graph; refs; listen; history; text; internal format)

	OFFSET	`0,6`
	LINKS	`Alois P. Heinz, Antidiagonals n = 0..140, flattened`
	EXAMPLE	`A(3,0) = 2: [3], [1,1,1].` `A(4,1) = 6: [4], [2,2], [2,1,1], [1,2,1], [1,1,2], [1,1,1,1].` `A(5,2) = 5: [5], [3,1,1], [1,3,1], [1,1,3], [1,1,1,1,1].` `A(6,3) = 7: [6], [4,1,1], [3,3], [2,2,2], [1,4,1], [1,1,4], [1,1,1,1,1,1].` `Square array A(n,k) begins:` `1, 1, 1, 1, 1, 1, 1, 1, ...` `1, 1, 1, 1, 1, 1, 1, 1, ...` `2, 2, 2, 2, 2, 2, 2, 2, ...` `2, 4, 2, 2, 2, 2, 2, 2, ...` `3, 6, 5, 3, 3, 3, 3, 3, ...` `2, 11, 5, 4, 2, 2, 2, 2, ...` `4, 17, 10, 7, 6, 4, 4, 4, ...` `2, 29, 10, 8, 5, 4, 2, 2, ...`
	MAPLE	`b:= proc(n, i, k) option remember;` `if`(n<1 or i<1, 0, `if`(n=i, 1, add(b(n-i, i+j, k), j={-k, 0, k}))) `end:` A:= (n, k)-> `if`(n=0, 1, add(b(n, j, k), j=1..n)): `seq (seq (A(n, d-n), n=0..d), d=0..15);`
	CROSSREFS	`Column k=0 and diagonal give: A000005.` `Columns k=1, 2 give: A034297, A214253.` `Cf. A214247, A214248, A214249, A214257, A214258, A214268, A214269.` `Sequence in context: A138015 A103444 A099172 * A214257 A214248 A152719` `Adjacent sequences: A214243 A214244 A214245 * A214247 A214248 A214249`
	KEYWORD	`nonn,tabl`
	AUTHOR	`Alois P. Heinz, Jul 08 2012`
	STATUS	`approved`

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Last modified May 24 13:46 EDT 2013. Contains 225621 sequences.