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

0,2

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).

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A099390.

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

Sequence in context: A320336 A133284 A012570 * A160294 A092145 A278628

Adjacent sequences: A256041 A256042 A256043 * A256045 A256046 A256047

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 14 2015

Extensions

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

Status

approved