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6th row of array in A099390.
2

%I #32 Sep 08 2022 08:46:11

%S 1,13,281,6728,167089,4213133,106912793,2720246633,69289288909,

%T 1765722581057,45005025662792,1147185247901449,29242880940226381,

%U 745439797095329713,19002353776441540177,484398978524471931341,12348080425980866090537,314771823879840325570888

%N 6th row of array in A099390.

%H Alois P. Heinz, <a href="/A256044/b256044.txt">Table of n, a(n) for n = 0..700</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (40,-416,1224,-1224,416,-40,1).

%F G.f.: -(x^6 - 27*x^5 + 177*x^4 - 328*x^3 + 177*x^2 - 27*x + 1) / ((x - 1)*(x^3 - 26*x^2 + 13*x - 1)*(x^3 - 13*x^2 + 26*x - 1)). - _Alois P. Heinz_, Mar 16 2015

%F a(n) = 40*a(n-1) - 416*a(n-2) + 1224*a(n-3) - 1224*a(n-4) + 416*a(n-5) - 40*a(n-6) + a(n-7). - _Vincenzo Librandi_, Aug 20 2018

%t a[n_] := Product[2(2+Cos[2j Pi/7]+Cos[2k Pi/(2n+1)]), {k, 1, n}, {j, 1, 3}] // Round;

%t Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Aug 20 2018 *)

%t LinearRecurrence[{40, -416, 1224, -1224, 416, -40, 1}, {1, 13, 281, 6728, 167089, 4213133, 106912793}, 20] (* _Vincenzo Librandi_, Aug 20 2018 *)

%o (PARI) x='x+O('x^100); Vec(-(x^6-27*x^5+177*x^4-328*x^3+177*x^2-27*x+1)/((x-1)*(x^3-26*x^2+13*x-1)*(x^3-13*x^2+26*x-1))) \\ _Altug Alkan_, Mar 23 2016

%o (Magma) I:=[1,13,281,6728,167089,4213133,106912793]; [n le 7 select I[n] else 40*Self(n-1)-416*Self(n-2)+1224*Self(n-3)-1224*Self(n-4)+416*Self(n-5)-40*Self(n-6)+Self(n-7): n in [1..30]]; // _Vincenzo Librandi_, Aug 20 2018

%Y Cf. A099390.

%Y Bisection (even part) of A028468 and 6th row of A187596. - _Alois P. Heinz_, Mar 16 2015

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Mar 14 2015

%E a(8)-a(17) from _Alois P. Heinz_, Mar 16 2015