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A068236 First differences of (n+1)^5-n^5. 9
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 (list; graph; refs; listen; history; text; internal format)
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

Colin Barker, Table of n, a(n) for n = 0..1000

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.

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

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: A100430 A159653 A101098 * A054559 A331434 A042756

Adjacent sequences:  A068233 A068234 A068235 * A068237 A068238 A068239

KEYWORD

nonn,easy

AUTHOR

Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Mar 25 2002

STATUS

approved

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Last modified March 28 05:38 EDT 2020. Contains 333073 sequences. (Running on oeis4.)