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A105475
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Triangle read by rows: T(n,k) is number of compositions of n into k parts when each even part can be of two kinds.
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2
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1, 2, 1, 1, 4, 1, 2, 6, 6, 1, 1, 8, 15, 8, 1, 2, 11, 26, 28, 10, 1, 1, 12, 42, 64, 45, 12, 1, 2, 16, 60, 122, 130, 66, 14, 1, 1, 16, 82, 208, 295, 232, 91, 16, 1, 2, 21, 108, 324, 582, 621, 378, 120, 18, 1, 1, 20, 135, 480, 1035, 1404, 1176, 576, 153, 20, 1, 2, 26, 170, 675
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Riordan array ((1+2x)/(1-x^2),x(1+2x)/(1-x^2)). Factorises as ((1+2x)/(1-x^2),x)*(1,x(1+2x)/(1-x^2)). Row sums A105476 form an eigensequence for ((1+2x)/(1-x^2),x). [Paul Barry, Feb 10 2011]
Triangle T(n,k), 1<=k<=n, given by (0, 2, -3/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - DELEHAM Philippe, Jan 18 2012
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EXAMPLE
| T(4,2)=6 because we have (1,3),(3,1),(2,2),(2,2'),(2',2) and (2',2').
Triangle begins:
1;
2,1;
1,4,1;
2,6,6,1;
1,8,15,8,1;
Triangle (0, 2, -3/2, -1/2, 0, 0, 0...) DELTA (1, 0, 0, 0, 0, ...) begins :
1
0, 1
0, 2, 1
0, 1, 4, 1
0, 2, 6, 6, 1
0, 1, 8, 15, 8, 1
0, 2, 11, 26, 28, 10, 1
0, 1, 12, 42, 64, 45, 12, 1
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MAPLE
| G:=t*z*(1+2*z)/(1-t*z-z^2-2*t*z^2): Gser:=simplify(series(G, z=0, 14)): for n from 1 to 12 do P[n]:=sort(coeff(Gser, z^n)) od: for n from 1 to 12 do seq(coeff(P[n], t^k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
| Row sums yield A105476.
Cf. Diagonals : A000007, A000034, A000012, A005843, A000384, A100504
Sequence in context: A193554 A131350 A131087 * A144389 A136321 A112987
Adjacent sequences: A105472 A105473 A105474 * A105476 A105477 A105478
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KEYWORD
| nonn,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 09 2005
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