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A060887 a(n) = Sum_{j=0..12} n^j. 12
1, 13, 8191, 797161, 22369621, 305175781, 2612138803, 16148168401, 78536544841, 317733228541, 1111111111111, 3452271214393, 9726655034461, 25239592216021, 61054982558011, 139013933454241, 300239975158033, 619036127056621 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = Phi_13(n) where Let Phi_k is the k-th cyclotomic polynomial.

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

Index to values of cyclotomic polynomials of integer argument

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

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) { for (n=0, 1000, write("b060887.txt", 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

(Sage) [sum(n^j for j in (0..12)) for n in (0..20)] # G. C. Greubel, Apr 14 2019

CROSSREFS

Cf.  A053698, A053699, A053700, A053716, A053717, A102909, A103623, A060885, A102909, A104376, A104682, A105067.

Sequence in context: A210157 A213410 A013524 * A020521 A208169 A205162

Adjacent sequences:  A060884 A060885 A060886 * A060888 A060889 A060890

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 05 2001

EXTENSIONS

Name changed by G. C. Greubel, Apr 14 2019

STATUS

approved

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Last modified May 7 02:20 EDT 2021. Contains 343636 sequences. (Running on oeis4.)