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A256044 6th row of array in A099390. 2
1, 13, 281, 6728, 167089, 4213133, 106912793, 2720246633, 69289288909, 1765722581057, 45005025662792, 1147185247901449, 29242880940226381, 745439797095329713, 19002353776441540177, 484398978524471931341, 12348080425980866090537, 314771823879840325570888 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified March 4 20:58 EST 2021. Contains 341811 sequences. (Running on oeis4.)