A217534 a(n) = (n+3)^n - (3^n + 4^n + ... + (n+2)^n).

0, 0, 143, 3793, 84542, 1919704, 46627805, 1227528189, 35089362124, 1086720416752, 36332383035835, 1306095900888769, 50286217183755898, 2065817586807684432, 90239163524054501433, 4178002289972230821853, 204427003853886843251976, 10542316523726438001918616

Offset

2,3

Comments

The first two terms of the series illustrate the famous equalities 3^2 + 4^2 = 5^2 and 3^3 + 4^3 + 5^3 = 6^3. The following terms show how this eventually diverges.

Links

Table of n, a(n) for n=2..19.

Wikipedia, Number 143

Formula

a(n) = (n+3)^n - Sum_{k=3..n+2} k^n.

a(n) ~ k*n^n, where k = e^3/(e-1). - Charles R Greathouse IV, Oct 08 2012

Maple

a:= n-> (n+3)^n -add(k^n, k=3..n+2):
seq (a(n), n=2..20);  # Alois P. Heinz, Oct 08 2012

Mathematica

a[n_] := (n+3)^n + 2^n - HarmonicNumber[n+2, -n] + 1; Table[a[n], {n, 2, 20}] (* Jean-François Alcover, Feb 17 2014 *)
Table[(n+3)^n-Total[Range[3, n+2]^n], {n, 2, 20}] (* Harvey P. Dale, Sep 22 2019 *)

Prog

(PARI) a(n)=(n+3)^n-sum(k=3, n+2, k^n) \\ Charles R Greathouse IV, Oct 08 2012

Crossrefs

Sequence in context: A220292 A159054 A135946 * A279115 A199039 A199235

Adjacent sequences: A217531 A217532 A217533 * A217535 A217536 A217537

Keyword

nonn

Author

Philippe Beaudoin, Oct 05 2012

Status

approved