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

1,1

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).

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

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 *)

Prog

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

Crossrefs

Cf. A016269, A038719, A038720.

Sequence in context: A006043 A112328 A370732 * A308700 A064837 A224902

Adjacent sequences: A038718 A038719 A038720 * A038722 A038723 A038724

Keyword

nonn,easy

Author

N. J. A. Sloane, May 02 2000

Extensions

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

Status

approved