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

%I #10 Jul 18 2020 10:05:26

%S 0,441,35623,1561238,59287158,2165511047,78259307721,2820153607740,

%T 101551366735840,3656082204395957,131621033827371963,

%U 4738375497166097906,170581677602043334746,6140941779058210902771,221073915991189916489149,7958661078139728516094136

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

%H Andrew Howroyd, <a href="/A151656/b151656.txt">Table of n, a(n) for n = 1..500</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (55,-799,4381,-8884,7552,-2304).

%F a(n) = 36^n - (7*n + 1)*8^n + 7*n*(7*n + 1)/2. - _Andrew Howroyd_, May 06 2020

%F From _Colin Barker_, Jul 18 2020: (Start)

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

%F 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.

%F (End)

%o (PARI) a(n) = {36^n - (7*n + 1)*8^n + 7*n*(7*n + 1)/2} \\ _Andrew Howroyd_, May 06 2020

%o (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

%Y Cf. A151624.

%K nonn,easy

%O 1,2

%A _R. H. Hardin_, May 29 2009

%E Terms a(7) and beyond from _Andrew Howroyd_, May 06 2020

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Last modified August 3 05:17 EDT 2024. Contains 374875 sequences. (Running on oeis4.)