|
| |
|
|
A022917
|
|
Multinomial coefficient n!/ ([n/4]!, [(n+1)/4]!, [(n+2)/4]!, [(n+3)/4]!).
|
|
3
| |
|
|
1, 1, 2, 6, 24, 60, 180, 630, 2520, 7560, 25200, 92400, 369600, 1201200, 4204200, 15765750, 63063000, 214414200, 771891120, 2933186256, 11732745024, 41064607584, 150570227808, 577185873264, 2308743493056, 8245512475200
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Multinomial coefficients(TOP, BOTTOM), where TOP = n, BOTTOM = ( a b c d ) where a = [ n/4 ], b = [ n/4 ], c = [ n/4 ], d = [ n/4 ] if n==0 mod 4; a = [ n/4 ], b = [ n/4 ], c = [ n/4 ], d = [ n/4 ]+1 if n==1 mod 4; a = [ n/4 ], b = [ n/4 ], c = [ n/4 ]+1, d = [ n/4 ]+1 if n==2 mod 4; a = [ n/4 ], b = [ n/4 ]+1, c = [ n/4 ]+1, d = [ n/4 ]+1 if n==3 mod 4.
Number of permutation patterns modulo 4. This matches the multinomial formula. [From Olivier Gerard, Feb 25 2011]
Aso the number of permutations of n elements where p(k-4) < p(k) for all k. [Joerg Arndt, Jul 23 2011]
|
|
|
EXAMPLE
| Starting from n=5, several permutations have the same pattern mod 4. Both (4,1,5,2,3) and (4,5,1,2,3) have pattern (0,1,1,2,3) modulo 4.
|
|
|
MATHEMATICA
| Table[ n!/(Quotient[n, 4]!*Quotient[n + 1, 4]!*Quotient[n + 2, 4]!*
Quotient[n + 3, 4]!), {n, 0, 30}]
|
|
|
PROG
| (PARI) {a(n)= if(n<0, 0, n!/(n\4)!/((n+1)\4)!/((n+2)\4)!/((n+3)\4)!)} /* Michael Somos Jun 20 2007 */
|
|
|
CROSSREFS
| Cf. A001405 (permutation patterns mod 2).
Cf. A022916 (permutation patterns mod 3).
Sequence in context: A104114 A175624 A118038 * A189855 A189566 A178009
Adjacent sequences: A022914 A022915 A022916 * A022918 A022919 A022920
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
|
|
|
EXTENSIONS
| Corrected by Michael Somos, Jun 20 2007
|
| |
|
|
