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A022916
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Multinomial coefficient n!/([n/3]![(n+1)/3]![(n+2)/3]!).
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5
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1, 1, 2, 6, 12, 30, 90, 210, 560, 1680, 4200, 11550, 34650, 90090, 252252, 756756, 2018016, 5717712, 17153136, 46558512, 133024320, 399072960, 1097450640, 3155170590, 9465511770, 26293088250, 75957810500, 227873431500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of permutation patterns modulo 3. This matches the multinomial formula. [From Olivier Gerard, Feb 25 2011]
Also the number of permutations of n elements where p(k-3) < p(k) for all k. [Joerg Arndt, Jul 23 2011]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
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EXAMPLE
| Starting from n=4, several permutations have the same pattern. Both (3,1,4,2) and (3,4,1,2) have pattern (0, 1, 1, 2) modulo 3.
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MATHEMATICA
| Table[ n!/(Quotient[n, 3]!*Quotient[n + 1, 3]!*
Quotient[n + 2, 3]!), {n, 0, 30}]
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PROG
| (PARI) a(n)=n!/((n\3)!*((n+1)\3)!*((n+2)\3)!)
(PARI) {a(n)= if(n<0, 0, n!/(n\3)!/((n+1)\3)!/((n+2)\3)!)} /* Michael Somos Jun 20 2007 */
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CROSSREFS
| A006480(n) = A022916(3*n).
Cf. A001405 (permutation patterns mod 2).
Cf. A022917 (permutation patterns mod 4).
Sequence in context: A161507 A032177 A095349 * A073949 A080372 A163087
Adjacent sequences: A022913 A022914 A022915 * A022917 A022918 A022919
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Corrected by Michael Somos, Jun 20 2007
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