A256044 6th row of array in A099390.

1, 13, 281, 6728, 167089, 4213133, 106912793, 2720246633, 69289288909, 1765722581057, 45005025662792, 1147185247901449, 29242880940226381, 745439797095329713, 19002353776441540177, 484398978524471931341, 12348080425980866090537, 314771823879840325570888

Offset: 0

Author

N. J. A. Sloane, Mar 14 2015

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..700
• Index entries for linear recurrences with constant coefficients, signature (40,-416,1224,-1224,416,-40,1).

Crossrefs

Cf. A099390.

Bisection (even part) of A028468 and 6th row of A187596. - Alois P. Heinz, Mar 16 2015

Programs

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

Mathematica

a[n_] := Product[2(2+Cos[2j Pi/7]+Cos[2k Pi/(2n+1)]), {k, 1, n}, {j, 1, 3}] // Round;
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Aug 20 2018 *)
LinearRecurrence[{40, -416, 1224, -1224, 416, -40, 1}, {1, 13, 281, 6728, 167089, 4213133, 106912793}, 20] (* Vincenzo Librandi, Aug 20 2018 *)

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

Formula

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

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

Extensions

a(8)-a(17) from Alois P. Heinz, Mar 16 2015