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

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, ...,.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11476 (rows n = 1..150, flattened)

Index entries for sequences related to the Josephus Problem

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.

Sequence in context: A151847 A349593 A179743 * A109225 A112564 A244911

Adjacent sequences: A113746 A113747 A113748 * A113750 A113751 A113752

Keyword

nonn,tabl

Author

Paul D. Hanna and Robert G. Wilson v, Nov 05 2005

Status

approved