A240930 a(n) = n^7 - n^6.

0, 0, 64, 1458, 12288, 62500, 233280, 705894, 1835008, 4251528, 9000000, 17715610, 32845824, 57921708, 97883968, 159468750, 251658240, 386201104, 578207808, 846825858, 1216000000, 1715322420, 2380977984, 3256789558, 4395368448, 5859375000, 7722894400, 10072932714

Offset: 0

Author

Martin Renner, Aug 03 2014

Keywords

• nonn
• easy

Comments

For n>1 number of 7-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 (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A001014, A001015.

Cf. A002378, A045991, A085537, A085538, A085539, A240931, A240932, A240933.

Programs

Magma

[n^7-n^6 : n in [0..30]]; // Wesley Ivan Hurt, Aug 03 2014

Maple

A240930:=n->n^7-n^6: seq(A240930(n), n=0..30); # Wesley Ivan Hurt, Aug 03 2014

Mathematica

Table[n^7 - n^6, {n, 0, 30}] (* Wesley Ivan Hurt, Aug 03 2014 *)
CoefficientList[Series[2 (32*x^2 + 473*x^3 + 1208*x^4 + 718*x^5 + 88*x^6 + x^7)/(x - 1)^8, {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 03 2014 *)

PARI

vector(100, n, (n-1)^7 - (n-1)^6) \\ Derek Orr, Aug 03 2014

Formula

a(n) = n^6*(n-1) = n^7 - n^6.

a(n) = A001015(n) - A001014(n).

G.f.: 2*(32*x^2 + 473*x^3 + 1208*x^4 + 718*x^5 + 88*x^6 + x^7)/(x - 1)^8. - Wesley Ivan Hurt, Aug 03 2014

Recurrence: a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*(n-6)+8*a(n-7)-a(n-8). - Wesley Ivan Hurt, Aug 03 2014

Sum_{n>=2} 1/a(n) = 6 - Sum_{k=2..6} zeta(k). - Amiram Eldar, Jul 05 2020