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A068236 First differences of (n+1)^5-n^5.

%I A068236 #24 Jun 05 2019 10:46:49
%S A068236 30,180,570,1320,2550,4380,6930,10320,14670,20100,26730,34680,44070,
%T A068236 55020,67650,82080,98430,116820,137370,160200,185430,213180,243570,
%U A068236 276720,312750,351780,393930,439320,488070,540300,596130,655680,719070,786420,857850,933480
%N A068236 First differences of (n+1)^5-n^5.
%C A068236 For n>=0, a(n) is equal to the number of functions f:{1,2,3,4,5}->{1,2,...,n+2} such that Im(f) contains 2 fixed elements. - Aleksandar M. Janjic and _Milan Janjic_, Feb 24 2007
%H A068236 Colin Barker, <a href="/A068236/b068236.txt">Table of n, a(n) for n = 0..1000</a>
%H A068236 O. Bagdasar, <a href="http://www.np.ac.rs/downloads/publications/VOL6_Br_2/vol6br2-3.pdf">On some functions involving the lcm and gcd of integer tuples</a>, Scientific Publications of the State University of Novi Pazar, Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91--100.
%H A068236 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A068236 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A068236 a(n) = (n+2)^5-2*(n+1)^5+n^5.
%F A068236 a(n) = 30*A005900(n+1). - _R. J. Mathar_, Sep 02 2008
%F A068236 a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - _Colin Barker_, Dec 13 2014
%F A068236 G.f.: 30*(x+1)^2 / (x-1)^4. - _Colin Barker_, Dec 13 2014
%t A068236 Table[20*n^3 + 10*n, {n, 1, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 19 2011 *)
%t A068236 Differences[#[[2]]-#[[1]]&/@Partition[Range[0,40]^5,2,1]] (* or *) LinearRecurrence[{4,-6,4,-1},{30,180,570,1320},40] (* _Harvey P. Dale_, Jun 05 2019 *)
%o A068236 (PARI) Vec(30*(x+1)^2 / (x-1)^4 + O(x^100)) \\ _Colin Barker_, Dec 13 2014
%Y A068236 Cf. A022521 ((n+1)^5-n^5), A000584 (5th powers), A005900 (octahedral numbers).
%K A068236 nonn,easy
%O A068236 0,1
%A A068236 Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Mar 25 2002