A275831 a(n) = (sqrt(7)*csc(Pi/7)/2)^n + (-sqrt(7)*csc(2*Pi/7)/2)^n + (-sqrt(7)*csc(4*Pi/7)/2)^n.

3, 0, 14, 21, 98, 245, 833, 2401, 7546, 22638, 69629, 211288, 645869, 1966419, 6000099, 18286016, 55765626, 170002805, 518361494, 1580379017, 4818550093, 14691183577, 44792503770, 136568135690, 416385811429, 1269524476220, 3870677629833, 11801372013543, 35981414742371, 109704347503632, 334479507291398

Offset: 0

Author

Kai Wang, Aug 11 2016

Keywords

• nonn
• easy

Comments

(sqrt(7)*csc(Pi/7)/2), (-sqrt(7)*csc(2*Pi/7)/2) and (-sqrt(7)*csc(4*Pi/7)/2) are the roots of the polynomial x^3 - 7*x - 7. - Corrected by Colin Barker, Aug 12 2016

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,7,7).

Crossrefs

Cf. A274975, A275195, A275830.

Programs

Mathematica

RecurrenceTable[{a[0] == 3, a[1] == 0, a[2] == 14, a[n] == 7 a[n - 2] + 7 a[n - 3]}, a, {n, 0, 30}] (* Bruno Berselli, Aug 11 2016 *)
LinearRecurrence[{0,7,7},{3,0,14},40] (* Harvey P. Dale, Jan 01 2022 *)

PARI

Vec((3-7*x^2)/(1-7*x^2-7*x^3) + O(x^30)) \\ Colin Barker, Aug 12 2016

Formula

G.f.: (3 - 7*x^2)/(1 - 7*x^2 - 7*x^3). - Bruno Berselli, Aug 11 2016

a(n) = 7*a(n-2) + 7*a(n-3) with n>2, a(0)=3, a(1)=0, a(2)=14.

Extensions

Name and comment corrected by Colin Barker, Aug 12 2016