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A289692
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The number of partitions of [n] with exactly 2 blocks without peaks.
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4
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0, 1, 2, 4, 8, 15, 27, 48, 85, 150, 264, 464, 815, 1431, 2512, 4409, 7738, 13580, 23832, 41823, 73395, 128800, 226029, 396654, 696080, 1221536, 2143647, 3761839, 6601568, 11584945
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f.: x^2*(1 - x + x^2) / ((1 - x)*(1 - 2*x + x^2 - x^3)).
a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) for n>4. (End)
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MAPLE
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a := proc(n) option remember: if n = 1 then 0 elif n = 2 then 1 elif n=3 then 2 elif n=4 then 4 elif n >= 5 then 3*procname(n-1) -3*procname(n-2)+2*procname(n-3)-procname(n-4) fi; end:
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MATHEMATICA
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LinearRecurrence[{3, -3, 2, -1}, {0, 1, 2, 4}, 40] (* Vincenzo Librandi, Jan 26 2018 *)
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PROG
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(GAP) a:=[0, 1, 2, 4]; for n in [5..10^2] do a[n]:=3*a[n-1]-3*a[n-2]+2*a[n-3]-a[n-4]; od; a; # Muniru A Asiru, Jan 25 2018
(Magma) I:=[0, 1, 2, 4]; [n le 4 select I[n] else 3*Self(n-1)-3*Self(n-2)+2*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jan 26 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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