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

Author

R. H. Hardin, May 29 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A151624.

Programs

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

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)

Extensions

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