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 A048782 Smallest positive number of "triangular" shuffles of n(n+1)/2 cards needed to restore them to their original order. 2
 1, 1, 2, 6, 10, 84, 70, 24, 36, 330, 210, 288, 1428, 252, 10080, 13680, 1260, 19320, 2160, 22440, 1692152, 50400, 140760, 3071880, 284088, 608753236, 617760, 15600, 35287560, 214138080, 30240, 1866600, 58333800, 8637552, 4034916600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Lay out cards in a triangular array from left to right in rows with 1 card in row 1 (the top row), 2 cards in row 2, etc., then pick up by columns, in order from the top of the column to the bottom, first from column 1, then column 2, etc. See A122158 for analogous results for a different triangular shuffle. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..500 EXAMPLE For n=3, successive shuffles give: 1.......1.......1 2.3.....2.4.....2.3 4.5.6...3.5.6...4.5.6, returning the deck of 6 cards to its original order in 2 shuffles. Thus a(3)=2. PROG (PARI) Perm(n)={concat(vector(n, i, vectorsmall(i, j, i+n*(j-1)-j*(j-1)/2)))} Follow(s, f)={my(t=f(s), k=1); while(t>s, k++; t=f(t)); if(s==t, k, 0)} CyclePoly(n, x)={my(v=Perm(n), q=0); for(i=1, #v, my(l=Follow(i, j->v[j])); if(l, q+=x^l)); q} a(n)={my(q=CyclePoly(n, x), m=1); for(i=1, poldegree(q), if(polcoeff(q, i), m=lcm(m, i))); m} \\ Andrew Howroyd, Nov 12 2017 CROSSREFS Cf. A121052, A122158. Sequence in context: A093880 A080397 A322756 * A083458 A124621 A325237 Adjacent sequences:  A048779 A048780 A048781 * A048783 A048784 A048785 KEYWORD nonn AUTHOR John W. Layman, Jul 14 1999, Aug 22 2006 EXTENSIONS Edited by R. J. Mathar, Aug 02 2008 STATUS approved

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Last modified June 24 17:58 EDT 2019. Contains 324330 sequences. (Running on oeis4.)