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A141351
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a(n) = C(n) + 1 - 0^n where C(n) = A000108(n).
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7
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1, 2, 3, 6, 15, 43, 133, 430, 1431, 4863, 16797, 58787, 208013, 742901, 2674441, 9694846, 35357671, 129644791, 477638701, 1767263191, 6564120421, 24466267021, 91482563641, 343059613651, 1289904147325, 4861946401453, 18367353072153, 69533550916005
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OFFSET
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0,2
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COMMENTS
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For n >= 2, a(n) is the number of parking functions of size n avoiding the patterns 132, 213, 231, and 312. - Lara Pudwell, Apr 12 2023
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LINKS
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FORMULA
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G.f.: c(x) + x/(1-x), where c(x) is the g.f. of A000108.
Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(9*n-13)*a(n-2) +2*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Oct 15 2014
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MAPLE
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a:= n-> signum(n)+binomial(n+n, n)/(n+1):
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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