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A275831
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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.
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3
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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
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OFFSET
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0,1
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COMMENTS
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(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
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LINKS
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FORMULA
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a(n) = 7*a(n-2) + 7*a(n-3) with n>2, a(0)=3, a(1)=0, a(2)=14.
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MATHEMATICA
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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 *)
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PROG
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(PARI) Vec((3-7*x^2)/(1-7*x^2-7*x^3) + O(x^30)) \\ Colin Barker, Aug 12 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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