A113749 - OEIS

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A113749

Consider the generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next k multiples of n-1, n-2, ..., 1, for n>=1. Now construct the array, t, such that t(n,k) is the n-th and successively rounding up to the next k multiples. This sequence is the presentation of that array by reading the antidiagonals.

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 7, 6, 1, 1, 5, 10, 13, 10, 1, 1, 6, 13, 18, 19, 12, 1, 1, 7, 16, 25, 30, 27, 18, 1, 1, 8, 19, 30, 39, 42, 39, 22, 1, 1, 9, 22, 37, 48, 61, 58, 49, 30, 1, 1, 10, 25, 42, 61, 72, 79, 78, 63, 34, 1, 1, 11, 28, 49, 70, 87, 102, 103, 102, 79, 42, 1, 1, 12, 31 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,5`
	COMMENTS	`The determinant of t(i,j), i=1..n, j=1..n, n=1..inf. is: 1,1,0,0,0,0, ...,.` `The determinant of t(i,j), i=1..n, j=-1..n-2, n=1..inf. is: 1,1,0,0,0,0, ...,.`
	EXAMPLE	`1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...,.` `1, 2, 4, 6, 10, 12, 18, 22, 30, 34, 42, 48, 58, 60, 78, ...,.` `1, 3, 7, 13, 19, 27, 39, 49, 63, 79, 91, 109, 133, 147, 181, ...,.` `1, 4, 10, 18, 30, 42, 58, 78, 102, 118, 150, 174, 210, 240, 274, ...,.` `1, 5, 13, 25, 39, 61, 79, 103, 133, 169, 207, 241, 289, 331, 387, ...,.` `1, 6, 16, 30, 48, 72, 102, 132, 168, 210, 258, 318, 360, 418, 492, ...,.` `1, 7, 19, 37, 61, 87, 123, 163, 207, 253, 307, 373, 447, 511, 589, ...,.` `1, 8, 22, 42, 70, 102, 142, 192, 240, 298, 360, 438, 510, 612, 708, ...,.` `1, 9, 25, 49, 79, 121, 163, 219, 279, 349, 423, 507, 589, 687, 807, ...,.` `1, 10, 28, 54, 90, 132, 180, 240, 318, 394, 480, 570, 672, 778, 898, ...,.` `1, 11, 31, 61, 99, 147, 207, 271, 349, 439, 529, 643, 751, 867,1009, ...,.` `1, 12, 34, 66, 108, 162, 228, 298, 382, 480, 588, 708, 838, 972,1114, ...,.`
	MATHEMATICA	`f[n_, k_] := Fold[ #2*Ceiling[ #1/#2 + k] &, n, Reverse@Range[n - 1]]; Table[f[n - k + 1, k], {n, -1, 11}, {k, n, -1, -1}] // Flatten`
	CROSSREFS	`Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748; det. A113749.` `Sequence in context: A120013 A151847 A179743 * A109225 A112564 A197957` `Adjacent sequences: A113746 A113747 A113748 * A113750 A113751 A113752`
	KEYWORD	`nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 05 2005`

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Last modified February 15 04:23 EST 2012. Contains 205694 sequences.