A060885 a(n) = Sum_{j=0..10} n^j.

1, 11, 2047, 88573, 1398101, 12207031, 72559411, 329554457, 1227133513, 3922632451, 11111111111, 28531167061, 67546215517, 149346699503, 311505013051, 617839704241, 1172812402961, 2141993519227, 3780494710543, 6471681049901, 10778947368421, 17513875027111, 27824681019587

Offset: 0

Author

N. J. A. Sloane, May 05 2001

Keywords

• nonn
• easy

Comments

a(n) = Phi_11(n), where 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 (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).

Crossrefs

Cf. similar sequences of the type a(n) = Sum_{j=0..m} n^j are:

A000027 (m=1), A002061 (m=2), A053698 (m=3), A053699 (m=4), A053700 (m=5), A053716 (m=6), A053717 (m=7), A102909 (m=8), A103623 (m=9), this sequence (m=10), A105067 (m=11), A060887 (m=12), A104376 (m=13), A104682 (m=14), A105312 (m=15), A269442 (m=16), A269446 (m=18).

Programs

Magma

[(&+[n^j: j in [0..10]]): n in [0..20]]; // G. C. Greubel, Apr 15 2019

Maple

A060885 := proc(n)
        numtheory[cyclotomic](11,n) ;
end proc:
seq(A060885(n),n=0..20) ; # R. J. Mathar, Feb 07 2014

Mathematica

Join[{1},Table[Total[n^Range[0,10]],{n,20}]] (* Harvey P. Dale, Jun 19 2011 *)

PARI

a(n) = 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

a(n) = polcyclo(11, n); \\ Michel Marcus, Apr 06 2016

Sage

[sum(n^j for j in (0..10)) for n in (0..20)] # G. C. Greubel, Apr 15 2019

Formula

a(n) = n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.

G.f.: (1+x^2*(1981+x*(66496+x*(534898+x*(1364848+x*(1233970+ x*(389104+x*(36829+x*(672+x)))))))))/(1-x)^11. - Harvey P. Dale, Jun 19 2011