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A294693
Number of permutations of [n] avoiding {1243, 2314, 3412}.
0
1, 1, 2, 6, 21, 73, 238, 722, 2054, 5541, 14323, 35788, 87043, 207201, 484772, 1118334, 2550164, 5759101, 12899521, 28689880, 63419177, 139435017, 305102778, 664755562, 1442788402, 3120497429, 6727583999, 14461863108, 31004177695, 66303416497, 141465316864, 301184381814, 639949891424
OFFSET
0,3
LINKS
D. Callan, T. Mansour, Enumeration of small Wilf Classes avoiding 1342 and two other 4-letter patterns, arXiv:1708.00832 (2017). Table 1 No 77.
Index entries for linear recurrences with constant coefficients, signature (12,-63,190,-363,456,-377,198,-60,8).
FORMULA
O.g.f.: (1 - 11*x + 53*x^2 - 145*x^3 + 248*x^4 - 274*x^5 + 192*x^6 - 80*x^7 + 17*x^8)/((1 - 2*x)^3*(1 - x)^6).
a(n) = -n^5/120 + n^4/24 - n^3/24 + (3*2^n + 35)*n^2/24 + (35*2^n + 142)*n/40 - (7*2^n - 8). - Bruno Berselli, Nov 07 2017
MAPLE
p := 1-11*x+53*x^2-145*x^3+248*x^4-274*x^5+192*x^6-80*x^7+17*x^8 ;
q := (1-x)^6*(1-2*x)^3 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;
CROSSREFS
Sequence in context: A294763 A294798 A294799 * A116757 A116839 A294800
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Nov 07 2017
STATUS
approved