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Search: id:A128100
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| A128100 |
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Triangle read by rows: T(n,k) is the number of ways to tile a 2 X n rectangle with k pieces of 2 X 2 tiles and n-2k pieces of 1 X 2 tiles (0<=k<=floor(n/2)). |
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+0
1
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| 1, 1, 2, 1, 3, 2, 5, 5, 1, 8, 10, 3, 13, 20, 9, 1, 21, 38, 22, 4, 34, 71, 51, 14, 1, 55, 130, 111, 40, 5, 89, 235, 233, 105, 20, 1, 144, 420, 474, 256, 65, 6, 233, 744, 942, 594, 190, 27, 1, 377, 1308, 1836, 1324, 511, 98, 7, 610, 2285, 3522, 2860, 1295, 315, 35, 1, 987, 3970
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums are the Jacobsthal numbers (A001045). Column 0 yields the Fibonacci numbers (A000045); the other columns yield convolved Fibonacci numbers (A001629,A001628,A001872,A001873, etc.). Sum(k(T(n,k),k=0..floor(n/2))=A073371(n-2).
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FORMULA
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G.f.=1/[1-z-(1+t)z^2].
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EXAMPLE
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Triangle starts:
1;
1;
2,1;
3,2;
5,5,1;
8,10,3;
13,20,9,1;
21,38,22,4;
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MAPLE
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G:=1/(1-z-(1+t)*z^2): Gser:=simplify(series(G, z=0, 19)): for n from 0 to 16 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 0 to 16 do seq(coeff(P[n], t, j), j=0..floor(n/2)) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A001045, A000045, A001629, A001628, A001872, A001873, A073371.
Sequence in context: A034393 A068932 A151533 this_sequence A035579 A045931 A079974
Adjacent sequences: A128097 A128098 A128099 this_sequence A128101 A128102 A128103
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 18 2007
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