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 A052456 Number of magic series of order n. 10
 1, 1, 2, 8, 86, 1394, 32134, 957332, 35154340, 1537408202, 78132541528, 4528684996756, 295011186006282, 21345627856836734, 1698954263159544138, 147553846727480002824, 13888244935445960871352, 1408407905312396429259944, 153105374581396386625831530 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Henry Bottomley's narrowing gap could be confirmed for 2 < n <= 64. - Walter Trump, Jan 21 2005 A new algorithm was found by Robert Gerbicz. Now the enumeration of magic series of orders greater than 100 is possible. - Walter Trump, May 05 2006 REFERENCES M. Kraitchik, Magic Series. Section 7.13.3 in Mathematical Recreations, New York, W. W. Norton, pp. 143 and 183-186, 1942. LINKS T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 0..150 (from Gerbicz and Trump) H. Bottomley, Partition and composition calculator H. Bottomley and W. Trump, First 36 terms Walter Trump, Magic Squares. Eric Weisstein's World of Mathematics, Magic Series Eric Weisstein's World of Mathematics, Multimagic Series Robert Gerbicz, Walter Trump, First 150 terms Robert Gerbicz, C-program to generate the sequence FORMULA a(n) = A067059(n, n*(n-1)) = r(n, n*(n-1), n^2*(n-1)/2) where r(n, m, k) is a restricted partition function giving the number of partitions of k into at most n positive parts each no more than m. - Henry Bottomley, Feb 25 2002. It seems a(n) (at least for 2 t*((2*i - t + 1)/2) = 0; b[0, _, _] = 1; b[n_, i_, t_] := b[n, i, t] = b[n, i - 1, t] + If[n < i, 0, b[n - i, i - 1, t - 1]]; a[_, 0] = 1; a[0, _] = 0; a[n_, k_] :=  With[{s = k*(k*n + 1)}, If[Mod[s, 2] == 1, 0, b[s/2, k*n, k]]]; a[n_] := a[n] = a[n, n]; Table[Print[a[n]]; a[n], {n, 0, 18}] (* Jean-François Alcover, Aug 15 2013, after Alois P. Heinz *) CROSSREFS Cf. A007785, A052457, A052458. A100568 is the same sequence times n!. Main diagonal of A204459. - Alois P. Heinz, Jan 18 2012 Sequence in context: A136647 A306001 A261730 * A276991 A000532 A333366 Adjacent sequences:  A052453 A052454 A052455 * A052457 A052458 A052459 KEYWORD nonn,nice AUTHOR EXTENSIONS Edited and ten more terms from Henry Bottomley, Feb 16 2002 Terms through a(36) added to attached web page, Feb 04 2005 STATUS approved

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Last modified October 3 22:17 EDT 2022. Contains 357237 sequences. (Running on oeis4.)