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URL: https://oeis.org/A060887

⇱ A060887 - OEIS

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A060887
a(n) = Sum_{j=0..12} n^j.
13
1, 13, 8191, 797161, 22369621, 305175781, 2612138803, 16148168401, 78536544841, 317733228541, 1111111111111, 3452271214393, 9726655034461, 25239592216021, 61054982558011, 139013933454241, 300239975158033, 619036127056621, 1224880286215951, 2336276859014281, 4311578947368421
OFFSET
0,2
COMMENTS
a(n) = Phi_13(n) where Let Phi_k is the k-th cyclotomic polynomial.
FORMULA
a(n) = n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.
G.f.: (x^12 + 2718*x^11 + 363156*x^10 + 8452952*x^9 + 59276439*x^8 + 155812164*x^7 + 167537592*x^6 + 74214648*x^5 + 12642423*x^4 + 691406*x^3 + 8100*x^2 + 1)/(1-x)^13. - Colin Barker, Oct 29 2012
a(n) = (n^13-1)/(n-1) with a(1) = 13 = lim_{x->1} a(x). - M. F. Hasler, Dec 31 2012
MAPLE
A060887 := proc(n)
numtheory[cyclotomic](13, n) ;
end proc:
seq(A060887(n), n=0..20) ; # R. J. Mathar, Feb 11 2014
MATHEMATICA
Table[1 + Sum[n^j, {j, 1, 12}], {n, 0, 20}] (* G. C. Greubel, Apr 14 2019 *)
PROG
(PARI) a(n) = { n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 } \\ Harry J. Smith, Jul 14 2009
(PARI) A060887(n)=polcyclo(13, n) \\ M. F. Hasler, Dec 31 2012
(Magma) [(&+[n^j: j in [0..12]]): n in [0..20]]; // G. C. Greubel, Apr 14 2019
(SageMath) [sum(n^j for j in (0..12)) for n in (0..20)] # G. C. Greubel, Apr 14 2019
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 05 2001
EXTENSIONS
Name changed by G. C. Greubel, Apr 14 2019
STATUS
approved