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A000363
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Number of permutations of [n] with exactly 2 increasing runs of length at least 2.
(Formerly M4018 N1666)
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4
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5, 61, 479, 3111, 18270, 101166, 540242, 2819266, 14494859, 73802835, 373398489, 1881341265, 9453340172, 47417364268, 237571096820, 1189405165908, 5951965440609, 29775517732665, 148927275340835, 744793282001995
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OFFSET
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4,1
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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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Vincenzo Librandi, Table of n, a(n) for n = 4..1000
Index entries for linear recurrences with constant coefficients, signature (14,-75,196,-263,174,-45).
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FORMULA
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a(n) = (5^n-(2*n-1)*3^n+2*n^2-2*n-2)/16. - Vaclav Kotesovec, Nov 19 2012
G.f.: -x^4*(9*x-5)/((x-1)^3*(3*x-1)^2*(5*x-1)). - Vaclav Kotesovec, Nov 19 2012
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MATHEMATICA
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Table[(5^n-(2*n-1)*3^n+2*n^2-2*n-2)/16, {n, 4, 20}] (* Vaclav Kotesovec, Nov 19 2012 *)
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PROG
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(Magma) [(5^n-(2*n-1)*3^n+2*n^2-2*n-2)/16: n in [4..30]]; // Vincenzo Librandi, May 03 2013
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CROSSREFS
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Contribution from Johannes W. Meijer, May 24 2009: (Start)
The a(n) sequence equals the third left hand column of A008971.
The a(2*n) sequence equals the third left hand column of A160486.
(End)
Sequence in context: A060060 A183379 A345649 * A200956 A203358 A099666
Adjacent sequences: A000360 A000361 A000362 * A000364 A000365 A000366
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms and better definition from Jon E. Schoenfield, Mar 25 2010
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STATUS
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approved
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