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A151624
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Number of permutations of 2 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order.
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5
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0, 1, 48, 603, 5158, 37257, 247236, 1568215, 9703890, 59226357, 358722928, 2163496611, 13017647646, 78225458401, 469740168924, 2819689366191, 16922139539626, 101545622110989, 609314411814024, 3656015481903355, 21936500845191030, 131620291694585721
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OFFSET
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1,3
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (15,-84,226,-309,207,-54).
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FORMULA
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a(n) = 6^n - (2*n + 1)*3^n + n*(2*n + 1). - Andrew Howroyd, May 06 2020
From Colin Barker, Jul 16 2020: (Start)
G.f.: x^2*(1 + 33*x - 33*x^2 - 81*x^3) / ((1 - x)^3*(1 - 3*x)^2*(1 - 6*x)).
a(n) = 15*a(n-1) - 84*a(n-2) + 226*a(n-3) - 309*a(n-4) + 207*a(n-5) - 54*a(n-6) for n>6.
(End)
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PROG
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(PARI) a(n) = {6^n - (2*n + 1)*3^n + n*(2*n + 1)} \\ Andrew Howroyd, May 06 2020
(PARI) Vec(x^2*(1 + 33*x - 33*x^2 - 81*x^3) / ((1 - x)^3*(1 - 3*x)^2*(1 - 6*x)) + O(x^25)) \\ Colin Barker, Jul 16 2020
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CROSSREFS
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Column k=2 of A154283.
Sequence in context: A190601 A179404 A171343 * A187611 A160286 A008658
Adjacent sequences: A151621 A151622 A151623 * A151625 A151626 A151627
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KEYWORD
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nonn,easy
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AUTHOR
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R. H. Hardin, May 29 2009
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EXTENSIONS
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Terms a(12) and beyond from Andrew Howroyd, May 06 2020
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STATUS
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approved
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