A028244 a(n) = 4^(n-1) - 3*3^(n-1) + 3*2^(n-1) - 1 (essentially Stirling numbers of second kind).

0, 0, 0, 6, 60, 390, 2100, 10206, 46620, 204630, 874500, 3669006, 15195180, 62350470, 254135700, 1030793406, 4166023740, 16792841910, 67558001700, 271392695406, 1089054420300, 4366671742950, 17498055448500, 70086339807006

Offset

1,4

Comments

For n>=4, a(n) is equal to the number of functions f: {1,2,...,n-1}->{1,2,3,4} such that Im(f) contains 3 fixed elements. - Aleksandar M. Janjic and Milan Janjic, Feb 27 2007

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1661

K. S. Immink, Coding Schemes for Multi-Level Channels that are Intrinsically Resistant Against Unknown Gain and/or Offset Using Reference Symbols, Electronics Letters ( Volume: 50, Issue: 1, January 2 2014 ).

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for linear recurrences with constant coefficients, signature (10, -35, 50, -24).

Formula

a(n) = 6*S(n, 4) = 6*A000453(n). - Emeric Deutsch, May 02 2004

G.f.: 6x^4/((1-x)(1-2x)(1-3x)(1-4x)). - R. J. Mathar, Oct 23 2008

E.g.f.: (exp(4*x) - 4*exp(3*x) + 6*exp(2*x) - 4*exp(x) + 1)/4, with a(0) = 0. - Wolfdieter Lang, May 03 2017

a(n) = 2*A032263(n). - Alois P. Heinz, Jan 24 2018

Mathematica

Table[4^(n - 1) - 3*3^(n - 1) + 3*2^(n - 1) - 1, {n, 1, 30}] (* Stefan Steinerberger, Apr 13 2006 *)
Table[6*StirlingS2[n, 4], {n, 1, 30}] (* G. C. Greubel, Nov 19 2017 *)

Prog

(Magma) [4^(n-1) - 3*3^(n-1) + 3*2^(n-1) - 1: n in [1..30]]; // G. C. Greubel, Nov 19 2017
(PARI) for(n=1, 30, print1(6*stirling(n, 4, 2), ", ")) \\ G. C. Greubel, Nov 19 2017

Crossrefs

Cf. A000453, A008277, A032263, A163626.

Sequence in context: A006741 A120573 A260345 * A259817 A230842 A353039

Adjacent sequences: A028241 A028242 A028243 * A028245 A028246 A028247

Keyword

nonn

Author

N. J. A. Sloane, Doug McKenzie (mckfam4(AT)aol.com)

Status

approved