A038721 k=2 column of A038719.

2, 18, 110, 570, 2702, 12138, 52670, 223290, 931502, 3842058, 15718430, 63928410, 258885902, 1045076778, 4208939390, 16921719930, 67944897902, 272553908298, 1092539107550, 4377127901850, 17529428119502, 70180466208618, 280910134414910, 1124205363178170, 4498515962822702

Offset: 1

Author

N. J. A. Sloane, May 02 2000

Keywords

• nonn
• easy

Comments

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

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

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

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• O. Bagdasar, On Some Functions Involving the lcm and gcd of Integer Tuples, Scientific publications of the state university of Novi Pazar, Ser. A: Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91-100.
• K. S. Immink, Coding Schemes for Multi-Level Channels that are Intrinsically Resistant Against Unknown Gain and/or Offset Using Reference Symbols, Electronics Letters, Volume50, Issue1, January 2014, pp. 20-22.
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets.
• Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.
• Rajesh Kumar Mohapatra and Tzung-Pei Hong, On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences, Mathematics (2022) Vol. 10, No. 7, 1161.
• R. B. Nelsen and H. Schmidt, Jr., Chains in power sets, Math. Mag., 64 (1991), 23-31.
• Ambrosio Valencia-Romero and P. T. Grogan, The strategy dynamics of collective systems: Underlying hindrances beyond two-actor coordination, PLOS ONE 19(4): e0301394 (S1 Appendix).
• Index entries for sequences related to posets
• Index entries for linear recurrences with constant coefficients, signature (9,-26,24).

Crossrefs

Cf. A016269, A038719, A038720.

Programs

Haskell

import Data.List (transpose)
a038721 n = a038721_list !! (n-1)
a038721_list = (transpose a038719_tabl) !! 2
-- Reinhard Zumkeller, Jul 08 2012

Mathematica

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 *)

Formula

a(n) = 4^(n+1) - 2*3^(n+1) + 2^(n+1).

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

G.f.: -2*x/((2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Nov 27 2012

E.g.f.: 2*exp(2*x)*(1 - 3*exp(x) + 2*exp(2*x)). - Stefano Spezia, Jun 04 2024

a(n) = 2 * A016269(n-1). - Alois P. Heinz, Jun 04 2024

Extensions

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