

A094374


a(n)=(3^n1)/2+2^n.


3



1, 3, 8, 21, 56, 153, 428, 1221, 3536, 10353, 30548, 90621, 269816, 805353, 2407868, 7207221, 21588896, 64701153, 193972388, 581655021, 1744440776, 5232273753, 15694724108, 47079978021, 141231545456, 423677859153, 1271000023028
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OFFSET

0,2


COMMENTS

Binomial transform of A094373.
Row sums of A125103.  Paul Barry, Dec 04 2007
Let P(A) be the power set of an nelement set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which either x is a subset of y or y is a subset of x, or 1) x and y are disjoint and for which x is not a subset of y and y is not a subset of x, or 2) x = y.  Ross La Haye, Jan 11 2008


REFERENCES

Ross La Haye, Binary Relations on the Power Set of an nElement Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6
A. Prasad, Equivalence classes of nodes in trees and rational generating functions, arXiv preprint arXiv:1407.5284, 2014


LINKS

Table of n, a(n) for n=0..26.
Index to sequences with linear recurrences with constant coefficients, signature (6,11,6).


FORMULA

G.f.: (13x+x^2)/((1x)(12x)(13x)); a(n)=6a(n1)11a(n2)+6a(n3). a(n)=A003462(n)+A000079(n).
a(n)=sum{k=0..n, C(n,k)+2^k*C(n,k+1)};  Paul Barry, Dec 04 2007
a(n) = StirlingS2(n+1,3) + 2*StirlingS2(n+1,2) + 1.  Ross La Haye, Jan 11 2008
a(0)=1, a(1)=3, a(2)=8, a(n)=6*a(n1)11*a(n2)+6*a(n3).  Harvey P. Dale, Jul 22 2013


MATHEMATICA

Table[(3^n1)/2+2^n, {n, 0, 30}] (* or *) LinearRecurrence[{6, 11, 6}, {1, 3, 8}, 30] (* Harvey P. Dale, Jul 22 2013 *)


CROSSREFS

Cf. A000225, A000392, A000079.
Sequence in context: A128105 A085560 A243633 * A008909 A006835 A014318
Adjacent sequences: A094371 A094372 A094373 * A094375 A094376 A094377


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Apr 28 2004


STATUS

approved



