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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 (list; graph; refs; listen; history; text; internal format)
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 pre-image 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*(n-1)*(n^2+n+1) = A000583(n) - n = A002061(n+1) * A002378(n-1) = (n-1) * 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)/(1-x)^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^3-1), 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^4-n); ) } \\ Harry J. Smith, Jun 23 2009

(MAGMA) [n^4-n: 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

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)