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A000507
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Number of permutations of [n] with exactly 3 increasing runs of length at least 2.
(Formerly M5323 N2314)
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3
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61, 1385, 19028, 206276, 1949762, 16889786, 137963364, 1081702420, 8236142455, 61386982075, 450403628440, 3266265481144, 23480284103492, 167687984079924, 1191656966048088, 8436830209386360, 59563995267159825, 419628657826253805
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OFFSET
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6,1
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REFERENCES
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F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 260.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=6..23.
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FORMULA
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a(n) = (3*7^n-(6*n-9)*5^n+(6*n^2-18*n+3)*3^n-4*n^3+18*n^2-8*n-15)/192.
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MATHEMATICA
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t[n_, 0] = 1; t[n_, k_] /; k > n/2 = 0; t[n_, k_] /; k <= n/2 := t[n, k] = (2k+1) t[n-1, k] + (n-2k+1) t[n-1, k-1]; a[n_] := t[n, 3]; Table[a[n], {n, 6, 23}] (* Jean-François Alcover, Feb 09 2016 *)
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PROG
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(Magma) [(3*7^n-(6*n-9)*5^n+(6*n^2-18*n+3)*3^n-4*n^3+18*n^2-8*n-15)/192: n in [6..30]]; // Vincenzo Librandi, Feb 09 2016
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CROSSREFS
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From Johannes W. Meijer, May 24 2009: (Start)
The a(n) sequence equals the fourth left hand column of A008971.
The a(2*n) sequence equals the fourth left hand column of A160486.
(End)
Sequence in context: A154428 A262017 A060061 * A350974 A143011 A211213
Adjacent sequences: A000504 A000505 A000506 * A000508 A000509 A000510
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Definition changed for clarity and for consistency with A008971, and formula and additional terms added by Jon E. Schoenfield, Mar 26 2010
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STATUS
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approved
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