

A058895


a(n) = n^4  n.


12



0, 0, 14, 78, 252, 620, 1290, 2394, 4088, 6552, 9990, 14630, 20724, 28548, 38402, 50610, 65520, 83504, 104958, 130302, 159980, 194460, 234234, 279818, 331752, 390600, 456950, 531414, 614628, 707252, 809970, 923490, 1048544, 1185888, 1336302, 1500590, 1679580
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OFFSET

0,3


COMMENTS

a(n) is the number of ways to assign 4 different students to n different dorm rooms, each of which can hold at most 3 students. In other words, a(n) is the number of functions f:[4]>[n] with the size of the preimage set of each element of the codomain at most 3.  Dennis P. Walsh, Mar 21 2013
a(n) are the values of m that yield integer solutions to this family of equations: x = sqrt(m + sqrt(x)), which may also be viewed as an infinitely recursive radical. The real solutions for x at each m = a(n) is n^2, except at n = 1 (m = 0) where x = 0 or 1 is a solution.  Richard R. Forberg, Oct 15 2014


LINKS

Harry J. Smith, Table of n, a(n) for n = 0..2000
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for linear recurrences with constant coefficients, signature (5, 10, 10, 5, 1).


FORMULA

a(n) = n*(n1)*(n^2+n+1) = A000583(n)  n = A002061(n+1) * A002378(n1) = (n1) * A027444(n) = n * A024001
a(n) = 2*A027482(n).  Zerinvary Lajos, Jan 28 2008
a(n) = floor(n^7/(n^3+1)).  Gary Detlefs, Feb 11 2010
a(n)^3 = (a(n)/n)^4 + (a(n)/n)^3.  Vincenzo Librandi, Feb 23 2012
a(n)^3 +A068601(n)^3 +A033562(n)^3 = A185065(n)^3, for n>0.  Vincenzo Librandi, Mar 13 2012
G.f.: 2*x^2*(7+4*x+x^2)/(1x)^5.  Colin Barker, Apr 23 2012
a(n) = 14*C(n,2) + 36*C(n,3) + 24*C(n,4).  Dennis P. Walsh, Mar 21 2013


MAPLE

seq(n*(n^31), n=0..25) ; # R. J. Mathar, Dec 10 2015


MATHEMATICA

Table[n^4  n, {n, 0, 40}] (* and *) LinearRecurrence[{5, 10, 10, 5, 1}, {0, 0, 14, 78, 252}, 100] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *)


PROG

(Sage) [lucas_number1(3, n^2, n) for n in range(0, 34)] # Zerinvary Lajos, May 16 2009
(PARI) { for (n = 0, 2000, write("b058895.txt", n, " ", n^4n); ) } \\ Harry J. Smith, Jun 23 2009
(MAGMA) [n^4n: n in [0..40]]; // Vincenzo Librandi, Feb 23 2012


CROSSREFS

Cf. A027482, A068601, A033562, A185065.
Sequence in context: A050404 A044201 A044582 * A166842 A231241 A138401
Adjacent sequences: A058892 A058893 A058894 * A058896 A058897 A058898


KEYWORD

easy,nonn,changed


AUTHOR

Henry Bottomley, Jan 08 2001


STATUS

approved



