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A116730
Number of permutations of length n which avoid the patterns 321, 1342, 1423.
1
1, 2, 5, 12, 25, 48, 87, 152, 259, 434, 719, 1182, 1933, 3150, 5121, 8312, 13477, 21836, 35363, 57252, 92671, 149982, 242715, 392762, 635545, 1028378, 1663997, 2692452, 4356529, 7049064, 11405679, 18454832, 29860603, 48315530, 78176231, 126491862, 204668197
OFFSET
1,2
FORMULA
G.f.: x*(1 - x + x^2 + 2*x^3) / ((1 - x)^2*(1 - x - x^2)).
a(n) = 2*A000045(n+3)-3*n-2. - R. J. Mathar, Aug 05 2008
From Colin Barker, Oct 20 2017: (Start)
a(n) = 1 + (2^(1-n)*((1-sqrt(5))^n*(-2+sqrt(5)) + (1+sqrt(5))^n*(2+sqrt(5))))/sqrt(5) - 3*(1 + n).
a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n>4.
(End)
PROG
(PARI) Vec(x*(1 - x + x^2 + 2*x^3) / ((1 - x)^2*(1 - x - x^2)) + O(x^40)) \\ Colin Barker, Oct 20 2017
CROSSREFS
Sequence in context: A116731 A116722 A368638 * A240847 A166106 A067331
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
EXTENSIONS
Extended beyond a(30) by R. J. Mathar, Aug 05 2008
STATUS
approved