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A269442
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a(n) = n*(n^8 + 1)*(n^4 + 1)*(n^2 + 1)*(n + 1) + 1.
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14
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1, 17, 131071, 64570081, 5726623061, 190734863281, 3385331888947, 38771752331201, 321685687669321, 2084647712458321, 11111111111111111, 50544702849929377, 201691918794585181, 720867993281778161, 2345488209948553531, 7037580381120954241
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OFFSET
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0,2
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COMMENTS
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a(n) = Phi_17(n) where Phi_k(x) is the k-th cyclotomic polynomial.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1).
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FORMULA
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G.f.: (1 +130918*x^2 +62343506*x^3 +4646748160*x^4 +102074708252*x^5 +878064150546*x^6 +3419813860214*x^7 +6502752956958*x^8 +6232856389160*x^9 +3004612851498*x^10 +701875014878*x^11 +73106078368*x^12 +2893069436*x^13 +31542430*x^14 +43674*x^15 +x^16)/(1 - x)^17.
Sum_{n>=0} 1/a(n) = 1.05883117453...
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MATHEMATICA
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Table[Cyclotomic[17, n], {n, 0, 15}]
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PROG
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(Magma) [n*(n^8+1)*(n^4+1)*(n^2+1)*(n+1)+1: n in [0..20]]; // Vincenzo Librandi, Feb 27 2016
(Sage) [n*(n^8+1)*(n^4+1)*(n^2+1)*(n+1)+1 for n in (0..20)] # G. C. Greubel, Apr 24 2019
(GAP) List([0..20], n-> n*(n^8+1)*(n^4+1)*(n^2+1)*(n+1)+1) # G. C. Greubel, Apr 24 2019
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CROSSREFS
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Cf. similar sequences of the type Phi_k(n), where Phi_k is the k-th cyclotomic polynomial: A000012 (k=0), A023443 (k=1), A000027 (k=3), A002522 (k=4), A053699 (k=5), A002061 (k=6), A053716 (k=7), A002523 (k=8), A060883 (k=9), A060884 (k=10), A060885 (k=11), A060886 (k=12), A060887 (k=13), A060888 (k=14), A060889 (k=15), A060890 (k=16), this sequence (k=17), A060891 (k=18), A269446 (k=19).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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