|
Search: id:A138162
|
|
|
| A138162 |
|
Number of permutations of {1,2,...,n} containing exactly 4 occurrences of the 132 pattern. |
|
+0
3
|
|
| 12, 96, 526, 2593, 12165, 55482, 248509, 1099255, 4817998, 20968680, 90747564, 390927869, 1677551078, 7174848666, 30598014925, 130155932685, 552386655300, 2339526458640, 9890067346740, 41737405295250, 175859194700958
(list; graph; listen)
|
|
|
OFFSET
|
5,1
|
|
|
COMMENT
|
a(n)=A138160(n,4).
|
|
REFERENCES
|
M. Bona, Permutations with one or two 132-subsequences, Discrete Math., 181, 1998, 267-274. M. Bona, The number of permutations with exactly r 132-subsequences is P-recursive in the size, Adv. Appl. Math., 18, 1997, 510-522.
T. Mansour and A. Vainshtein, Counting occurrences of 132 in a permutation
|
|
FORMULA
|
a(n)=(n^9+102n^8-282n^7-12264n^6+32589n^5+891978n^4-7589428n^3+25452024n^2-39821760n+23950080)(2n-12)!/[24n!(n-6)! ] for n>=6, a(5)=12. G.f.=(1/2)[P(x) + Q(x)/(1-4x)^(7/2)], where P(x)=5x^4-7x^3+2x^2+8x-3, Q(x)=2x^9 +218x^8+1074x^7-1754x^6+388x^5+1087x^4-945x^3+320x^2-50x+3.
|
|
EXAMPLE
|
a(5)=12 because we have 12534, 12453, 14253, 14523, 13254, 13524, 15324, 14352, 31542, 21534, 21453, and 25143.
|
|
MAPLE
|
P:=5*x^4-7*x^3+2*x^2+8*x-3: Q:=2*x^9+218*x^8+1074*x^7-1754*x^6+388*x^5+1087*x^4-945*x^3+320*x^2-50*x+3: g:=(P+Q/(1-4*x)^(7/2))*1/2: gser:=series(g, x=0, 30): seq(coeff(gser, x, n), n=5..25);
|
|
CROSSREFS
|
Cf. A002054, A082970, A138160, A082971, A138163.
Adjacent sequences: A138159 A138160 A138161 this_sequence A138163 A138164 A138165
Sequence in context: A059154 A120658 A121627 this_sequence A073392 A038845 A059375
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 27 2008
|
|
|
Search completed in 0.002 seconds
|
