A240931 a(n) = n^8 - n^7.

0, 0, 128, 4374, 49152, 312500, 1399680, 4941258, 14680064, 38263752, 90000000, 194871710, 394149888, 752982204, 1370375552, 2392031250, 4026531840, 6565418768, 10407740544, 16089691302, 24320000000, 36021770820, 52381515648, 74906159834, 105488842752, 146484375000

Offset: 0

Author

Martin Renner, Aug 03 2014

Keywords

• nonn
• easy

Comments

For n>1 number of 8-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 (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A001015, A001016.

Cf. A002378, A045991, A085537, A085538, A085539, A240930, A240932, A240933.

Programs

Magma

[n^8-n^7 : n in [0..30]]; // Wesley Ivan Hurt, Aug 09 2014

Maple

A240931:=n->n^8-n^7: seq(A240931(n), n=0..30); # Wesley Ivan Hurt, Aug 09 2014

Mathematica

Table[n^8 - n^7, {n, 0, 30}] (* Wesley Ivan Hurt, Aug 09 2014 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,0,128,4374,49152,312500,1399680,4941258,14680064},30] (* Harvey P. Dale, Apr 29 2016 *)

PARI

vector(100, n, (n-1)^8 - (n-1)^7) \\ Derek Orr, Aug 03 2014

PARI

concat([0,0], Vec(-2*x^2*(x^6+183*x^5+2682*x^4+8422*x^3+7197*x^2+1611*x+64) / (x-1)^9 + O(x^100))) \\ Colin Barker, Aug 08 2014

Formula

a(n) = n^7*(n-1) = n^8 - n^7.

a(n) = A001016(n) - A001015(n).

G.f.: -2*x^2*(x^6+183*x^5+2682*x^4+8422*x^3+7197*x^2+1611*x+64) / (x-1)^9. - Colin Barker, Aug 08 2014

Sum_{n>=2} 1/a(n) = 7 - Sum_{k=2..7} zeta(k). - Amiram Eldar, Jul 05 2020