A228291 a(n) = Sum_{k=1..7} n^k.

0, 7, 254, 3279, 21844, 97655, 335922, 960799, 2396744, 5380839, 11111110, 21435887, 39089244, 67977559, 113522234, 183063615, 286331152, 435984839, 648232974, 943531279, 1347368420, 1891142967, 2613136834, 3559590239, 4785883224, 6357828775, 8353082582

Offset: 0

Author

Alois P. Heinz, Aug 19 2013

Keywords

• nonn
• easy

Links

• Alois P. Heinz, 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

Column k=7 of A228275.

Programs

Maple

a:= n-> `if`(n=1, 7, (n^8-n)/(n-1)):
seq(a(n), n=0..30);

Mathematica

Table[Total[n^Range[7]],{n,0,30}] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,7,254,3279,21844,97655,335922,960799},30] (* Harvey P. Dale, Dec 06 2018 *)

R

a <- c(0, 7, 254, 3279, 21844, 97655, 335922, 960799)
for(n in (length(a)+1):30) a[n] <- 8*a[n-1] -28*a[n-2] +56*a[n-3] -70*a[n-4] +56*a[n-5] -28*a[n-6] +8*a[n-7] -a[n-8]
a  [Yosu Yurramendi, Sep 03 2013]

Formula

G.f.: x*(x^6+78*x^5+981*x^4+2332*x^3+1443*x^2+198*x+7)/(x-1)^8.

a(1) = 7, else a(n) = (n^8-n)/(n-1).

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) with n > 7, a(0)=0, a(1)=7, a(2)=254, a(3)=3279, a(4)=21844, a(5)=97655, a(6)=335922, a(7)=960799. - Yosu Yurramendi, Sep 03 2013