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A121548
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Triangle read by rows: T(n,k) is the number of compositions of n into k Fibonacci numbers (1<=k<=n; only one 1 is considered as a Fibonacci number).
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3
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1, 1, 1, 1, 2, 1, 0, 3, 3, 1, 1, 2, 6, 4, 1, 0, 3, 7, 10, 5, 1, 0, 2, 9, 16, 15, 6, 1, 1, 2, 9, 23, 30, 21, 7, 1, 0, 2, 10, 28, 50, 50, 28, 8, 1, 0, 3, 9, 34, 71, 96, 77, 36, 9, 1, 0, 2, 12, 36, 95, 156, 168, 112, 45, 10, 1, 0, 0, 12, 43, 115, 231, 308, 274, 156, 55, 11, 1, 1, 2, 9, 48, 140
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Sum of terms in row n = A076739(n). T(n,1)=A010056(n) (the characteristic function of the Fibonacci numbers); T(n,2)=A121549(n); T(n,3)=A121550(n); Sum(k*T(n,k), k=1..n)=A121551(n).
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FORMULA
| G.f.=G(t,z)=1/[1-t*Sum(z^fibonacci(i), i=2..infinity)]-1.
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EXAMPLE
| T(5,3)=6 because we have [1,2,2], [2,1,2], [2,2,1], [1,1,3], [1,3,1] and [3,1,1].
Triangle starts:
1;
1,1;
1,2,1;
0,3,3,1;
1,2,6,4,1;
0,3,7,10,5,1;
0,2,9,16,15,6,1;
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MAPLE
| with(combinat): G:=1/(1-t*sum(z^fibonacci(i), i=2..40))-1: Gser:=simplify(series(G, z=0, 25)): for n from 1 to 23 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 1 to 15 do seq(coeff(P[n], t, j), j=1..n) od; # yields sequence in triangular form
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CROSSREFS
| Cf. A076739, A010056, A121549, A121550, A121551.
Sequence in context: A107238 A055830 A079123 * A180179 A113020 A127258
Adjacent sequences: A121545 A121546 A121547 * A121549 A121550 A121551
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KEYWORD
| nonn,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 07 2006
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