cp's OEIS Frontend

A038721 k=2 column of A038719.

%I A038721 #74 Jun 05 2024 04:25:34
%S A038721 2,18,110,570,2702,12138,52670,223290,931502,3842058,15718430,
%T A038721 63928410,258885902,1045076778,4208939390,16921719930,67944897902,
%U A038721 272553908298,1092539107550,4377127901850,17529428119502,70180466208618,280910134414910,1124205363178170,4498515962822702
%N A038721 k=2 column of A038719.
%C A038721 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 A038721 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|. - _Ross La Haye_, Mar 19 2009
%C A038721 Number of ordered (n+1)-tuples of positive integers, whose minimum is 0 and maximum 3. - _Ovidiu Bagdasar_, Sep 19 2014
%C A038721 a(n-2) is the number of possible player-reduced binary games observed by each player in an n X 2 game assuming k < n - 1 players reverse their initially fixed individual strategies and the remaining n - k - 1 players will play as one, either maintaining their status quo strategies or jointly adopting an alternative strategy. - _Ambrosio Valencia-Romero_, Apr 11 2024
%H A038721 Reinhard Zumkeller, <a href="/A038721/b038721.txt">Table of n, a(n) for n = 1..1000</a>
%H A038721 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 A038721 K. S. Immink, <a href="https://doi.org/10.1049/el.2013.3558">Coding Schemes for Multi-Level Channels that are Intrinsically Resistant Against Unknown Gain and/or Offset Using Reference Symbols</a>, Electronics Letters, Volume50, Issue1, January 2014, pp. 20-22.
%H A038721 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>.
%H A038721 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 A038721 Rajesh Kumar Mohapatra and Tzung-Pei Hong, <a href="https://doi.org/10.3390/math10071161">On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences</a>, Mathematics (2022) Vol. 10, No. 7, 1161.
%H A038721 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 A038721 Ambrosio Valencia-Romero and P. T. Grogan, <a href="https://doi.org/10.1371/journal.pone.0301394">The strategy dynamics of collective systems: Underlying hindrances beyond two-actor coordination</a>, PLOS ONE 19(4): e0301394 (<a href="https://doi.org/10.1371/journal.pone.0301394.s001">S1 Appendix</a>).
%H A038721 <a href="/index/Pos#posets">Index entries for sequences related to posets</a>
%H A038721 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-26,24).
%F A038721 a(n) = 4^(n+1) - 2*3^(n+1) + 2^(n+1).
%F A038721 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 A038721 G.f.: -2*x/((2*x-1)*(3*x-1)*(4*x-1)). - _Colin Barker_, Nov 27 2012
%F A038721 E.g.f.: 2*exp(2*x)*(1 - 3*exp(x) + 2*exp(2*x)). - _Stefano Spezia_, Jun 04 2024
%F A038721 a(n) = 2 * A016269(n-1). - _Alois P. Heinz_, Jun 04 2024
%t A038721 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 A038721 (Haskell)
%o A038721 import Data.List (transpose)
%o A038721 a038721 n = a038721_list !! (n-1)
%o A038721 a038721_list = (transpose a038719_tabl) !! 2
%o A038721 -- _Reinhard Zumkeller_, Jul 08 2012
%Y A038721 Cf. A016269, A038719, A038720.
%K A038721 nonn,easy
%O A038721 1,1
%A A038721 _N. J. A. Sloane_, May 02 2000
%E A038721 More terms from Larry Reeves (larryr(AT)acm.org), May 09 2000