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A068236
First differences of (n+1)^5-n^5.
10
30, 180, 570, 1320, 2550, 4380, 6930, 10320, 14670, 20100, 26730, 34680, 44070, 55020, 67650, 82080, 98430, 116820, 137370, 160200, 185430, 213180, 243570, 276720, 312750, 351780, 393930, 439320, 488070, 540300, 596130, 655680, 719070, 786420, 857850, 933480
OFFSET
0,1
COMMENTS
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
LINKS
O. Bagdasar, On some functions involving the lcm and gcd of integer tuples, Scientific Publications of the State University of Novi Pazar, Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91--100.
FORMULA
a(n) = (n+2)^5-2*(n+1)^5+n^5.
a(n) = 30*A005900(n+1). - R. J. Mathar, Sep 02 2008
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Colin Barker, Dec 13 2014
G.f.: 30*(x+1)^2 / (x-1)^4. - Colin Barker, Dec 13 2014
MATHEMATICA
Table[20*n^3 + 10*n, {n, 1, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)
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 *)
PROG
(PARI) Vec(30*(x+1)^2 / (x-1)^4 + O(x^100)) \\ Colin Barker, Dec 13 2014
CROSSREFS
Cf. A022521 ((n+1)^5-n^5), A000584 (5th powers), A005900 (octahedral numbers).
Sequence in context: A159653 A369855 A101098 * A331434 A054559 A335634
KEYWORD
nonn,easy
AUTHOR
Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Mar 25 2002
STATUS
approved