A240932 a(n) = n^9 - n^8.

0, 0, 256, 13122, 196608, 1562500, 8398080, 34588806, 117440512, 344373768, 900000000, 2143588810, 4729798656, 9788768652, 19185257728, 35880468750, 64424509440, 111612119056, 187339329792, 305704134738, 486400000000, 756457187220, 1152393344256, 1722841676182

Offset: 0

Author

Martin Renner, Aug 03 2014

Keywords

• nonn
• easy

Comments

For n>1 number of 9-digit positive integers in base n.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A001016, A001017.

Cf. A002378, A045991, A085537, A085538, A085539, A240930, A240931, A240933.

Programs

Magma

[n^9-n^8: n in [0..40]]; // Vincenzo Librandi, Aug 15 2016

Mathematica

Table[n^9 - n^8, {n, 0, 40}] (* Vincenzo Librandi, Aug 15 2016 *)

PARI

vector(100, n, (n-1)^9 - (n-1)^8) \\ Derek Orr, Aug 03 2014

Formula

a(n) = n^8*(n-1) = n^9 - n^8.

a(n) = A001017(n) - A001016(n).

G.f.: 2*x^2*(x^7+374*x^6+9327*x^5+49780*x^4+78095*x^3+38454*x^2+5281*x+128) / (x-1)^10. - Colin Barker, Aug 08 2014

Sum_{n>=2} 1/a(n) = 8 - Sum_{k=2..8} zeta(k). - Amiram Eldar, Jul 05 2020