A152499 1/12 of the number of permutations of 3 indistinguishable copies of 1..n with exactly 2 local maxima.

0, 1, 30, 664, 13632, 274432, 5497344, 109987840, 2199945216, 43999756288, 879998926848, 17599995314176, 351999979683840, 7039999912443904, 140799999624609792, 2815999998397775872, 56319999993188450304, 1126399999971143188480, 22527999999878130302976

Offset

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (28,-176,320).

Formula

a(n) = (11*20^(n-1) - 11*4^(n-1) - 12*(n-1)*4^(n-1))/128. - Andrew Howroyd, May 10 2020

From Colin Barker, Jul 15 2020: (Start)

G.f.: x^2*(1 + 2*x) / ((1 - 4*x)^2*(1 - 20*x)).

a(n) = 28*a(n-1) - 176*a(n-2) + 320*a(n-3) for n>2.

(End)

Prog

(PARI) a(n) = {(11*20^(n-1) - 11*4^(n-1) - 12*(n-1)*4^(n-1))/128} \\ Andrew Howroyd, May 10 2020
(PARI) concat(0, Vec(x^2*(1 + 2*x) / ((1 - 4*x)^2*(1 - 20*x)) + O(x^40))) \\ Colin Barker, Jul 15 2020

Crossrefs

Cf. A152494, A334773.

Sequence in context: A111779 A075473 A051563 * A027475 A180801 A035520

Adjacent sequences: A152496 A152497 A152498 * A152500 A152501 A152502

Keyword

nonn,easy

Author

R. H. Hardin, Dec 06 2008

Extensions

Terms a(10) and beyond from Andrew Howroyd, May 10 2020

Status

approved