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A238731
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Riordan array ((1-2*x)/(1-3*x+x^2), x/(1-3*x+x^2)).
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11
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1, 1, 1, 2, 4, 1, 5, 13, 7, 1, 13, 40, 33, 10, 1, 34, 120, 132, 62, 13, 1, 89, 354, 483, 308, 100, 16, 1, 233, 1031, 1671, 1345, 595, 147, 19, 1, 610, 2972, 5561, 5398, 3030, 1020, 203, 22, 1, 1597, 8495, 17984, 20410, 13893, 5943, 1610, 268, 25, 1, 4181
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OFFSET
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0,4
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COMMENTS
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Unsigned version of A124037 and A126126.
Subtriangle of the triangle given by (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
Row sums are A001075(n).
Diagonal sums are A133494(n).
Sum_{k=0..n} T(n,k)*x^k = A001519(n), A001075(n), A002320(n), A038723(n), A033889(n) for x = 0, 1, 2, 3, 4 respectively. - Philippe Deléham, Mar 05 2014
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LINKS
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Table of n, a(n) for n=0..55.
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FORMULA
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T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - T(n-2,k), T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.
G.f.: (1-2*x)/(1-(y+3)*x+x^2). - Philippe Deléham, Mar 05 2014
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EXAMPLE
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Triangle begins:
1;
1, 1;
2, 4, 1;
5, 13, 7, 1;
13, 40, 33, 10, 1;
34, 120, 132, 62, 13, 1;
89, 354, 483, 308, 100, 16, 1;
233, 1031, 1671, 1345, 595, 147, 19, 1;...
Triangle (0, 1, 1, 1, 0, 0, 0, ...) DELTA (1, 0, 2, -2, 0, 0, ...) begins:
1;
0, 1;
0, 1, 1;
0, 2, 4, 1;
0, 5, 13, 7, 1;
0, 13, 40, 33, 10, 1;
0, 34, 120, 132, 62, 13, 1;
0, 89, 354, 483, 308, 100, 16, 1;
0, 233, 1031, 1671, 1345, 595, 147, 19, 1;...
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MATHEMATICA
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(* The function RiordanArray is defined in A256893. *)
RiordanArray[(1-2#)/(1-3#+#^2)&, x/(1-3#+#^2)&, 10] // Flatten (* Jean-François Alcover, Jul 16 2019 *)
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CROSSREFS
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Cf. A001519, A000012, A016777, A062708.
Cf. A001906, A124037, A126126.
Sequence in context: A085059 A336164 A181336 * A124037 A126126 A090285
Adjacent sequences: A238728 A238729 A238730 * A238732 A238733 A238734
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KEYWORD
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nonn,tabl
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AUTHOR
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Philippe Deléham, Mar 03 2014
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STATUS
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approved
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