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A085583
Number of (3412,1234)-avoiding involutions in S_n.
0
1, 2, 4, 8, 16, 29, 51, 83, 131, 196, 286, 402, 554, 743, 981, 1269, 1621, 2038, 2536, 3116, 3796, 4577, 5479, 6503, 7671, 8984, 10466, 12118, 13966, 16011, 18281, 20777, 23529, 26538, 29836, 33424, 37336, 41573, 46171, 51131, 56491, 62252, 68454, 75098
OFFSET
1,2
FORMULA
a(n) = (2*n^4-4*n^3+28*n^2-2*n+81-6*n*(-1)^n+15*(-1)^n)/96.
G.f.: -x*(x^6-2*x^5+x^4+3*x^3-x^2-x+1) / ((x-1)^5*(x+1)^2). - Colin Barker, Jul 16 2013
a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7). - Wesley Ivan Hurt, Jan 20 2024
MATHEMATICA
CoefficientList[Series[-(x^6 - 2*x^5 + x^4 + 3*x^3 - x^2 - x + 1)/((x - 1)^5*(x + 1)^2), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jan 20 2024 *)
CROSSREFS
Sequence in context: A177269 A018726 A049884 * A160786 A054154 A292793
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Jul 06 2003
EXTENSIONS
More terms from Colin Barker, Jul 16 2013
STATUS
approved