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
Examples
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, ...,.
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
Crossrefs
Programs
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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
Comments