A102909 a(n) = Sum_{j=0..8} n^j.

1, 9, 511, 9841, 87381, 488281, 2015539, 6725601, 19173961, 48427561, 111111111, 235794769, 469070941, 883708281, 1589311291, 2745954241, 4581298449, 7411742281, 11668193551, 17927094321, 26947368421, 39714002329, 57489010371, 81870575521, 114861197401

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = (n^2+n+1) * (n^6+n^3+1) and so is never prime. - Jonathan Vos Post, Dec 21 2012

G.f.: (x^8 + 162*x^7 + 3418*x^6 + 14212*x^5 + 16578*x^4 + 5482*x^3 + 466*x^2 + 1)/(1-x)^9. - Colin Barker, Nov 05 2012, edited by M. F. Hasler, Dec 31 2012

a(n) = (n^9-1)/(n-1) with a(1) = 9. - L. Edson Jeffery and M. F. Hasler, Dec 30 2012

Mathematica

1 + Sum[Range[0, 30]^j, {j, 1, 8}] (* G. C. Greubel, Feb 13 2018 *)

Prog

(PARI) a(n)=n^8+n^7+n^6+n^5+n^4+n^3+n^2+n+1 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [(&+[n^j: j in [0..8]]): n in [0..30]]; // G. C. Greubel, Feb 13 2018
(Sage) [sum(n^j for j in (0..8)) for n in (0..30)] # G. C. Greubel, Apr 14 2019

Crossrefs

Cf. A001016, A060890, A059839.

Cf. similar sequences of the type a(n) = Sum_{j=0..m} n^j: A000027 (m=1), A002061 (m=2), A053698 (m=3), A053699 (m=4), A053700 (m=5), A053716 (m=6), A053717 (m=7), this sequence (m=8), A103623 (m=9), A060885 (m=10), A105067 (m=11), A060887 (m=12), A104376 (m=13), A104682 (m=14), A105312 (m=15), A269442 (m=16), A269446 (m=18).

Sequence in context: A332149 A112910 A180585 * A367552 A230671 A281443

Adjacent sequences: A102906 A102907 A102908 * A102910 A102911 A102912

Keyword

nonn,easy

Author

Douglas Winston (douglas.winston(AT)srupc.com), Mar 01 2005

Extensions

Offset corrected by N. J. A. Sloane, Dec 30 2012

Status

approved