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A038721 k=2 column of A038719. 4
2, 18, 110, 570, 2702, 12138, 52670, 223290, 931502, 3842058, 15718430, 63928410, 258885902, 1045076778, 4208939390, 16921719930, 67944897902, 272553908298, 1092539107550, 4377127901850, 17529428119502, 70180466208618 (list; graph; refs; listen; history; text; internal format)
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|. [From 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

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, 2013.

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.

R. B. Nelsen and H. Schmidt, Jr., Chains in power sets, Math. Mag., 64 (1991), 23-31.

Index entries for sequences related to posets

Index entries for linear recurrences with constant coefficients, signature (9,-26,24).

FORMULA

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

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. A038720.

Sequence in context: A101570 A006043 A112328 * 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

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Last modified November 14 17:22 EST 2019. Contains 329126 sequences. (Running on oeis4.)