A269486 a(n) = Sum_{j=0..10} (-n)^j.
1, 1, 683, 44287, 838861, 8138021, 51828151, 247165843, 954437177, 3138105961, 9090909091, 23775972551, 57154490053, 128011456717, 269971011311, 540609741211, 1034834473201, 1903994239313, 3382547898907, 5824512944911
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)
- Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
- Index to values of cyclotomic polynomials of integer argument
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
Crossrefs
Cf. similar sequences of the type Phi_k(n) listed in A269442.
Programs
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GAP
List([0..20], n-> Sum([0..10], j-> (-n)^j)); # G. C. Greubel, Apr 24 2019
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Magma
[n^10-n^9+n^8-n^7+n^6-n^5+n^4-n^3+n^2-n+1: n in [0..30]]; // Vincenzo Librandi, Feb 29 2016
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Mathematica
Table[Cyclotomic[22, n], {n, 0, 19}] CoefficientList[Series[(1 -10x +727x^2 +36664x^3 +389434x^4 +1233508x^5 + 1365310 x^6 +534568x^7 +66661x^8 +1926x^9 +11x^10)/(1-x)^11, {x,0,33}], x] (* Vincenzo Librandi, Feb 29 2016 *) -
PARI
a(n) = polcyclo(22, n); \\ Michel Marcus, Feb 28 2016
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Sage
[sum((-n)^j for j in (0..10)) for n in (0..20)] # G. C. Greubel, Apr 24 2019
Formula
G.f.: (1 - 10*x + 727*x^2 + 36664*x^3 + 389434*x^4 + 1233508*x^5 + 1365310*x^6 + 534568*x^7 + 66661*x^8 + 1926*x^9 + 11*x^10)/(1-x)^11. - Vincenzo Librandi, Feb 29 2016
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).
Sum_{n>=0} 1/a(n) = 2.0014880486975...
Extensions
Name changed by G. C. Greubel, Apr 24 2019
Comments