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A066810
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Expansion of x^2/((1-3*x)*(1-2*x)^2).
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7
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0, 0, 1, 7, 33, 131, 473, 1611, 5281, 16867, 52905, 163835, 502769, 1532883, 4651897, 14070379, 42456897, 127894979, 384799049, 1156756443, 3475250065, 10436235955, 31330727961, 94038321227, 282211432673, 846835624611
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Binomial transform of A000295.
a(n) = A112626(n, 2). - Ross La Haye (rlahaye(AT)new.rr.com), Jan 11 2006
Let Q be a binary relation on the power set P(A) of a set A having n = |A| elements such that for all x,y of P(A), xQy if x is a proper subset of y and |y| - |x| > 1. Then a(n) = |Q|. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 11 2008
a(n) is the number of n-digit ternary sequences that have at least two 0's. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Apr 14 2009]
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REFERENCES
| 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. [From Ross La Haye (rlahaye(AT)new.rr.com), Feb 22 2009]
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LINKS
| Harry J. Smith, Table of n, a(n) for n = 0..200
Index to sequences with linear recurrences with constant coefficients, signature (7,-16,12)
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FORMULA
| a(n) = 3^n - 2^n - n*2^(n-1)
a(n) = A000244(n) - A001792(n). a(n) = Sum[C(n,k)2^(n-k),{k,2,n}]. - Ross La Haye (rlahaye(AT)new.rr.com), Apr 26 2006
Inverse binomial transform of A086443. - Ross La Haye (rlahaye(AT)new.rr.com), Apr 29 2006
Convolution of A000244 beginning [0,1,3,9,27,81...] and A001787. - Ross La Haye (rlahaye(AT)new.rr.com), Feb 15 2007
E.g.f.:exp(2x)(exp(x)-x-1). a(n)= 3*a(n-1)+(n-1)*2^(n-2) [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Apr 14 2009]
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MATHEMATICA
| RecurrenceTable[{a[n] == 3*a[n - 1] + (n - 1) 2^(n - 2), a[0] == 0}, a, {n, 0, 20}] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Apr 14 2009]
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PROG
| (PARI) { for (n=0, 200, write("b066810.txt", n, " ", 3^n - 2^n - n*2^(n-1)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Mar 29 2010]
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CROSSREFS
| Sequence in context: A100855 A000605 A114014 * A034577 A141291 A089106
Adjacent sequences: A066807 A066808 A066809 * A066811 A066812 A066813
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 25 2002
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EXTENSIONS
| Additional comments from Ross La Haye (rlahaye(AT)new.rr.com), Sep 27 2005
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