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A130810
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If X_1,...,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 4-subsets of X containing none of X_i, (i=1,...n).
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4
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16, 80, 240, 560, 1120, 2016, 3360, 5280, 7920, 11440, 16016, 21840, 29120, 38080, 48960, 62016, 77520, 95760, 117040, 141680, 170016, 202400, 239200, 280800, 327600, 380016, 438480, 503440, 575360, 654720, 742016, 837760, 942480, 1056720
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,1
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COMMENTS
| Number of n permutations (n>=4)of 3 objects u,v,z, with repetition allowed, containing n-4 u's. Example: if n=4 then n-4 =(0) zero u, a(1)=16 because we have vvvv zzzz vvvz zzzv vvzv zzvz vzvv zvzz zvvv vzzz vvzz zzvv vzvz zvzv zvvz vzzv [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 05 2008]
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REFERENCES
| H. J. Brothers, Pascal's Prism: Supplementary Material, http://www.brotherstechnology.com/docs/Pascal's_Prism_(supplement).pdf.
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LINKS
| Milan Janjic, Two Enumerative Functions
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FORMULA
| a(n)=binomial(2*n,4)+binomial(n,2)-n*binomial(2*n-2,2)
a(n)=C(n,n-4)*2^4,n>=4. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 07 2007
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MAPLE
| a:=n->binomial(2*n, 4)+binomial(n, 2)-n*binomial(2*n-2, 2);
seq(binomial(n, n-4)*2^4, n=4..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 07 2007
(Maple) seq(binomial(n+3, 4)*2^4, n=1..12); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 05 2008]
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CROSSREFS
| A038207, A000079, A001787, A001788, A001789, A003472, A054849, A002409, A054851, A140325, A140354, A046092, A130809 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 05 2008]
Sequence in context: A044584 A111732 A008511 * A050468 A068778 A034570
Adjacent sequences: A130807 A130808 A130809 * A130811 A130812 A130813
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KEYWORD
| nonn
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AUTHOR
| Milan R. Janjic (agnus(AT)blic.net), Jul 16 2007
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