A060894 a(n) = n^8 + n^7 - n^5 - n^4 - n^3 + n + 1.

1, 1, 331, 8401, 80581, 464881, 1950271, 6568801, 18837001, 47763361, 109889011, 233669041, 465542221, 878077201, 1580623591, 2732936641, 4562284561, 7384587841, 11630180251, 17874821521, 26876632021, 39619660081, 57364832911, 81709082401, 114653477401, 158681234401

Offset: 0

Author

N. J. A. Sloane, May 05 2001

Keywords

• nonn
• easy

Comments

a(n) = Phi_30(n) where Phi_k(x) is the k-th cyclotomic polynomial.

Links

• Harry J. Smith, Table of n, a(n) for n=0,...,1000
• Hisanori Mishima, Factorizations of many number sequences
• Index to values of cyclotomic polynomials of integer argument
• Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Programs

Maple

A060894 := proc(n)
        numtheory[cyclotomic](30,n) ;
end proc:
seq(A060894(n),n=0..20) ; # R. J. Mathar, Feb 11 2014

Mathematica

Table[n^8+n^7-n^5-n^4-n^3+n+1,{n,0,30}] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,1,331,8401,80581,464881,1950271,6568801,18837001},30] (* Harvey P. Dale, Apr 07 2019 *)

PARI

a(n) = { n^8 + n^7 - n^5 - n^4 - n^3 + n + 1 } \\ Harry J. Smith, Jul 14 2009

Formula

G.f.: (1-8*x+358*x^2+5374*x^3+16930*x^4+14284*x^5+3238*x^6+142*x^7+x^8)/ (1-x)^9. - Colin Barker, Apr 21 2012