A294698 Number of permutations of [n] avoiding {1423, 1234, 3412}.

1, 1, 2, 6, 21, 74, 248, 780, 2309, 6483, 17407, 45028, 112921, 275964, 660030, 1550320, 3586449, 8190493, 18500893, 41399992, 91896773, 202564062, 443789172, 967093220, 2097536909, 4530328551, 9748157339, 20905142940, 44695397953, 95295673696, 202670082154

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

D. Callan, T. Mansour, Enumeration of small Wilf Classes avoiding 1342 and two other 4-letter patterns, arXiv:1708.00832 [math.CO] (2017). Table 1 No 118.

Index entries for linear recurrences with constant coefficients, signature (13,-75,253,-553,819,-833,575,-258,68,-8).

Formula

G.f.: (1 - 12*x + 64*x^2 - 198*x^3 + 393*x^4 - 521*x^5 + 463*x^6 - 269*x^7 + 95*x^8 - 17*x^9) / ((1 - x)^7*(1 - 2*x)^3).

From Colin Barker, Nov 07 2017: (Start)

a(n) = (1/720)*(720*(41 - 5*2^(3+n)) + 6*(2812 + 465*2^n)*n + 2*(2627 + 45*2^n)*n^2 + 765*n^3 + 145*n^4 + 3*n^5 + n^6).

a(n) = 13*a(n-1) - 75*a(n-2) + 253*a(n-3) - 553*a(n-4) + 819*a(n-5) - 833*a(n-6) + 575*a(n-7) - 258*a(n-8) + 68*a(n-9) - 8*a(n-10) for n > 9. (End)

Maple

p := 1-12*x+64*x^2-198*x^3+393*x^4-521*x^5+463*x^6-269*x^7+95*x^8-17*x^9 ;
q := (1-x)^7*(1-2*x)^3 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;

Prog

(PARI) Vec((1 - 12*x + 64*x^2 - 198*x^3 + 393*x^4 - 521*x^5 + 463*x^6 - 269*x^7 + 95*x^8 - 17*x^9) / ((1 - x)^7*(1 - 2*x)^3) + O(x^40)) \\ Colin Barker, Nov 07 2017

Crossrefs

Sequence in context: A294765 A116745 A116831 * A294766 A116752 A294767

Adjacent sequences: A294695 A294696 A294697 * A294699 A294700 A294701

Keyword

nonn,easy

Author

R. J. Mathar, Nov 07 2017

Status

approved