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A232396
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Triangular array read by rows: T(n,k) is the number of compositions of n with no two consecutive identical parts that have exactly k parts = 1, n>=0, 0<=k<=ceiling(n/3).
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2
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1, 0, 1, 1, 0, 1, 2, 1, 2, 1, 3, 3, 1, 3, 8, 3, 6, 9, 7, 1, 7, 20, 10, 2, 14, 27, 25, 5, 18, 52, 39, 14, 1, 30, 77, 78, 26, 3, 45, 132, 133, 60, 8, 66, 213, 240, 117, 24, 1, 107, 334, 421, 232, 54, 4, 157, 562, 716, 450, 127, 12, 245, 872, 1265, 842, 279, 38, 1
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OFFSET
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0,7
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LINKS
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FORMULA
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G.f.: 1/( 1 - y*x/(1 + y*x) - Sum_{j>=2} x^j/(1 + x^j) ).
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EXAMPLE
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1;
0, 1;
1, 0;
1, 2;
1, 2, 1;
3, 3, 1;
3, 8, 3;
6, 9, 7, 1;
7, 20, 10, 2;
14, 27, 25, 5;
18, 52, 39, 14, 1;
T(7,2) = 7 because we have: 1+2+1+3, 1+2+3+1, 1+3+1+2, 1+3+2+1, 1+5+1, 2+1+3+1, 3+1+2+1.
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MAPLE
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b:= proc(n, t) option remember; `if`(n=0, 1, expand(
add(`if`(j=t, 0, b(n-j, j)*`if`(j=1, x, 1)), j=1..n)))
end:
T:= n-> seq(coeff(b(n, 0), x, i), i=0..ceil(n/3)):
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MATHEMATICA
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nn=10; CoefficientList[Series[1/(1- u z/(1+ u z) - Sum[z^j/(1+z^j), {j, 2, nn}]), {z, 0, nn}], {z, u}]//Grid
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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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STATUS
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approved
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