A151624 Number of permutations of 2 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order.

0, 1, 48, 603, 5158, 37257, 247236, 1568215, 9703890, 59226357, 358722928, 2163496611, 13017647646, 78225458401, 469740168924, 2819689366191, 16922139539626, 101545622110989, 609314411814024, 3656015481903355, 21936500845191030, 131620291694585721

Offset

1,3

Links

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).

Formula

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)

E.g.f.: x*(3+2*x)*exp(x) - (1+6*x)*exp(3*x) + exp(6*x). - G. C. Greubel, Jun 19 2022

Mathematica

Table[6^n -(2*n+1)*3^n +n*(2*n+1), {n, 40}] (* G. C. Greubel, Jun 19 2022 *)

Prog

(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
(Magma) [(&+[(-1)^j*Binomial(2*n+1, 2-j)*Binomial(j+2, 2)^n: j in [0..2]]): n in [1..40]]; // G. C. Greubel, Jun 19 2022
(SageMath) [6^n -(2*n+1)*3^n +binomial(2*n+1, 2) for n in (1..40)] # G. C. Greubel, Jun 19 2022

Crossrefs

Column k=2 of A154283.

Sequence in context: A190601 A179404 A171343 * A187611 A362235 A160286

Adjacent sequences: A151621 A151622 A151623 * A151625 A151626 A151627

Keyword

nonn,easy

Author

R. H. Hardin, May 29 2009

Extensions

Terms a(12) and beyond from Andrew Howroyd, May 06 2020

Status

approved