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%I #17 Oct 01 2022 08:22:51
%S 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,
%T 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,
%U 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
%N 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.
%C The determinant of t(i,j), i=1..n, j=1..n, n=1..inf. is: 1,1,0,0,0,0, ...,.
%C The determinant of t(i,j), i=1..n, j=-1..n-2, n=1..inf. is: 1,1,0,0,0,0, ...,.
%H Michael De Vlieger, <a href="/A113749/b113749.txt">Table of n, a(n) for n = 1..11476</a> (rows n = 1..150, flattened)
%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...,.
%e 1, 2, 4, 6, 10, 12, 18, 22, 30, 34, 42, 48, 58, 60, 78, ...,.
%e 1, 3, 7, 13, 19, 27, 39, 49, 63, 79, 91, 109, 133, 147, 181, ...,.
%e 1, 4, 10, 18, 30, 42, 58, 78, 102, 118, 150, 174, 210, 240, 274, ...,.
%e 1, 5, 13, 25, 39, 61, 79, 103, 133, 169, 207, 241, 289, 331, 387, ...,.
%e 1, 6, 16, 30, 48, 72, 102, 132, 168, 210, 258, 318, 360, 418, 492, ...,.
%e 1, 7, 19, 37, 61, 87, 123, 163, 207, 253, 307, 373, 447, 511, 589, ...,.
%e 1, 8, 22, 42, 70, 102, 142, 192, 240, 298, 360, 438, 510, 612, 708, ...,.
%e 1, 9, 25, 49, 79, 121, 163, 219, 279, 349, 423, 507, 589, 687, 807, ...,.
%e 1, 10, 28, 54, 90, 132, 180, 240, 318, 394, 480, 570, 672, 778, 898, ...,.
%e 1, 11, 31, 61, 99, 147, 207, 271, 349, 439, 529, 643, 751, 867,1009, ...,.
%e 1, 12, 34, 66, 108, 162, 228, 298, 382, 480, 588, 708, 838, 972,1114, ...,.
%t 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
%Y Cf. {k=-1..12} A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748.
%K nonn,tabl
%O 1,5
%A _Paul D. Hanna_ and _Robert G. Wilson v_, Nov 05 2005
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