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A027082
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Irregular triangular array: T(n,0) = 1 for n >= 1; T(n,1) = T(n,2) = 1 for n >= 1; T(n,k) = T(n-1,k-3) + T(n-1,k-2) + T(n-1,k-1) for 3 <= k <= 2n-1 and n >= 2; and T(n,2n) = T(n-1,2n-3) + T(n-1,2n-2) for n >= 2.
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33
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1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 3, 5, 6, 5, 1, 1, 1, 3, 5, 9, 14, 16, 11, 1, 1, 1, 3, 5, 9, 17, 28, 39, 41, 27, 1, 1, 1, 3, 5, 9, 17, 31, 54, 84, 108, 107, 68, 1, 1, 1, 3, 5, 9, 17, 31, 57, 102, 169, 246, 299, 283, 175, 1, 1, 1, 3, 5, 9, 17, 31, 57
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listen;
history;
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internal format)
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OFFSET
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0,8
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LINKS
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EXAMPLE
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The first 6 rows:
1
1 .. 1 .. 1
1 .. 1 .. 1 .. 3 .. 2
1 .. 1 .. 1 .. 3 .. 5 .. 6 .. 5
1 .. 1 .. 1 .. 3 .. 5 .. 9 .. 14 .. 16 .. 11
1 .. 1 .. 1 .. 3 .. 5 .. 9 .. 17 .. 28 .. 39 .. 41 .. 27
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MAPLE
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option remember;
if k < 0 or k > 2*n then
0;
elif k <=2 then
1;
elif k = 2*n then
procname(n-1, k-3)+procname(n-1, k-2) ;
else
procname(n-1, k-3)+procname(n-1, k-2)+procname(n-1, k-1) ;
end if;
end proc:
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MATHEMATICA
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t[n_, 0] := 1; t[n_, 1] := 1; t[n_, 2] := 1; t[n_, k_] := t[n, k] = If[k < 2 n, t[n - 1, k - 3] + t[n - 1, k - 2] + t[n - 1, k - 1], t[n - 1, 2 n - 3] + t[n - 1, 2 n - 2]]; u = Table[t[n, k], {n, 0, 10}, {k, 0, 2 n}]; v = Flatten[u] (* A027082 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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Offset corrected to 0 and b-file recomputed by R. J. Mathar, Jun 24 2020
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STATUS
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approved
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