A151640 Number of permutations of 4 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order.

0, 36, 1828, 40136, 693960, 11000300, 168594156, 2550000528, 38371094416, 576250000820, 8647558594740, 129734375001176, 1946130371095128, 29192578125001596, 437892028808595580, 6568398437500002080, 98526072692871096096, 1477891601562500002628

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (28,-253,976,-1675,1300,-375).

Formula

a(n) = 15^n - (4*n + 1)*5^n + 2*n*(4*n + 1). - Andrew Howroyd, May 06 2020

From Colin Barker, May 06 2020: (Start)

G.f.: 4*x^2*(9 + 205*x - 485*x^2 - 625*x^3) / ((1 - x)^3*(1 - 5*x)^2*(1 - 15*x)).

a(n) = 28*a(n-1) - 253*a(n-2) + 976*a(n-3) - 1675*a(n-4) + 1300*a(n-5) - 375*a(n-6) for n > 6. (End)

E.g.f.: exp(15*x) - (1+20*x)*exp(5*x) + 2*x*(5+4*x)*exp(x). - G. C. Greubel, Sep 08 2022

Mathematica

Table[Sum[(-1)^j*Binomial[4*n+1, j]*Binomial[6-j, 4]^n, {j, 0, 2}], {n, 30}] (* G. C. Greubel, Sep 08 2022 *)

Prog

(PARI) a(n) = {15^n - (4*n + 1)*5^n + 2*n*(4*n + 1)} \\ Andrew Howroyd, May 06 2020
(PARI) concat(0, Vec(4*x^2*(9 + 205*x - 485*x^2 - 625*x^3) / ((1 - x)^3*(1 - 5*x)^2*(1 - 15*x)) + O(x^20))) \\ Colin Barker, May 07 2020
(Magma) [15^n -(4*n+1)*5^n +2*n*(4*n+1): n in [1..30]]; // G. C. Greubel, Sep 08 2022
(SageMath) [15^n -(4*n+1)*5^n +2*n*(4*n+1) for n in (1..30)] # G. C. Greubel, Sep 08 2022

Crossrefs

Column k=2 of A236463.

Sequence in context: A054980 A391281 A391282 * A025754 A071128 A065782

Adjacent sequences: A151637 A151638 A151639 * A151641 A151642 A151643

Keyword

nonn,easy

Author

R. H. Hardin, May 29 2009

Extensions

Terms a(9) and beyond from Andrew Howroyd, May 06 2020

Status

approved