A151656 Number of permutations of 7 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order.

0, 441, 35623, 1561238, 59287158, 2165511047, 78259307721, 2820153607740, 101551366735840, 3656082204395957, 131621033827371963, 4738375497166097906, 170581677602043334746, 6140941779058210902771, 221073915991189916489149, 7958661078139728516094136

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (55,-799,4381,-8884,7552,-2304).

Formula

a(n) = 36^n - (7*n + 1)*8^n + 7*n*(7*n + 1)/2. - Andrew Howroyd, May 06 2020

From Colin Barker, Jul 18 2020: (Start)

G.f.: 49*x^2*(9 + 232*x - 932*x^2 - 1024*x^3) / ((1 - x)^3*(1 - 8*x)^2*(1 - 36*x)).

a(n) = 55*a(n-1) - 799*a(n-2) + 4381*a(n-3) - 8884*a(n-4) + 7552*a(n-5) - 2304*a(n-6) for n>6.

(End)

Prog

(PARI) a(n) = {36^n - (7*n + 1)*8^n + 7*n*(7*n + 1)/2} \\ Andrew Howroyd, May 06 2020
(PARI) concat(0, Vec(49*x^2*(9 + 232*x - 932*x^2 - 1024*x^3) / ((1 - x)^3*(1 - 8*x)^2*(1 - 36*x)) + O(x^40))) \\ Colin Barker, Jul 18 2020

Crossrefs

Cf. A151624.

Sequence in context: A221248 A220680 A189278 * A264088 A264277 A268874

Adjacent sequences: A151653 A151654 A151655 * A151657 A151658 A151659

Keyword

nonn,easy

Author

R. H. Hardin, May 29 2009

Extensions

Terms a(7) and beyond from Andrew Howroyd, May 06 2020

Status

approved