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 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
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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). 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. 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 *) PROG (PARI) Vec((3-7*x^2)/(1-7*x^2-7*x^3) + O(x^30)) \\ Colin Barker, Aug 12 2016 CROSSREFS Cf. A274975, A275195, A275830. Sequence in context: A323689 A321413 A135399 * A065121 A334824 A167339 Adjacent sequences: A275828 A275829 A275830 * A275832 A275833 A275834 KEYWORD nonn,easy AUTHOR Kai Wang, Aug 11 2016 EXTENSIONS Name and comment corrected by Colin Barker, Aug 12 2016 STATUS approved

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Last modified September 22 08:11 EDT 2023. Contains 365519 sequences. (Running on oeis4.)