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 A217534 a(n) = (n+3)^n - (3^n + 4^n + ... + (n+2)^n). 0
 0, 0, 143, 3793, 84542, 1919704, 46627805, 1227528189, 35089362124, 1086720416752, 36332383035835, 1306095900888769, 50286217183755898, 2065817586807684432, 90239163524054501433, 4178002289972230821853, 204427003853886843251976, 10542316523726438001918616 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 8 23:37 EST 2023. Contains 367681 sequences. (Running on oeis4.)