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A038721 k=2 column of A038719. 4


%S 2,18,110,570,2702,12138,52670,223290,931502,3842058,15718430,

%T 63928410,258885902,1045076778,4208939390,16921719930,67944897902,

%U 272553908298,1092539107550,4377127901850,17529428119502,70180466208618

%N k=2 column of A038719.

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

%C Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if x is not a subset of y and y is not a subset of x. Then a(n+1) = |R|. [From _Ross La Haye_, Mar 19 2009]

%C Number of ordered (n+1)-tuples of positive integers, whose minimum is 0 and maximum 3. - _Ovidiu Bagdasar_, Sep 19 2014

%H Reinhard Zumkeller, <a href="/A038721/b038721.txt">Table of n, a(n) for n = 1..1000</a>

%H O. Bagdasar, <a href="http://www.np.ac.rs/downloads/publications/VOL6_Br_2/vol6br2-3.pdf">On Some Functions Involving the lcm and gcd of Integer Tuples</a>, Scientific publications of the state university of Novi Pazar, Ser. A: Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91-100.

%H K. S. Immink, <a href="http://www.exp-math.uni-essen.de/~immink/pdf/jsac13.pdf">Coding Schemes for Multi-Level Channels that are Intrinsically Resistant Against Unknown Gain and/or Offset Using Reference Symbols</a>, 2013.

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>

%H Ross La Haye, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/LaHaye/lahaye5.html">Binary Relations on the Power Set of an n-Element Set</a>, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.

%H R. B. Nelsen and H. Schmidt, Jr., <a href="http://www.jstor.org/stable/2690450">Chains in power sets</a>, Math. Mag., 64 (1991), 23-31.

%H <a href="/index/Pos#posets">Index entries for sequences related to posets</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (9,-26,24).

%F 4^(n+1) - 2*3^(n+1) + 2^(n+1).

%F a(1)=2, a(2)=18, a(3)=110, a(n)=9*a(n-1)-26*a(n-2)+24*a(n-3). - _Harvey P. Dale_, Aug 16 2012

%F G.f.: -2*x/((2*x-1)*(3*x-1)*(4*x-1)). - _Colin Barker_, Nov 27 2012

%t Table[4^n-2*3^n+2^n,{n,2,30}] (* or *) LinearRecurrence[{9,-26,24},{2,18,110},30] (* _Harvey P. Dale_, Aug 16 2012 *)

%o (Haskell)

%o import Data.List (transpose)

%o a038721 n = a038721_list !! (n-1)

%o a038721_list = (transpose a038719_tabl) !! 2

%o -- _Reinhard Zumkeller_, Jul 08 2012

%Y Cf. A038720.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, May 02 2000

%E More terms from Larry Reeves (larryr(AT)acm.org), May 09 2000

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Last modified December 18 18:07 EST 2018. Contains 318243 sequences. (Running on oeis4.)