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A055801
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Array T read by rows: T(i,0)=T(i,i)=1 for i >= 0; T(i,j)=Sum{T(i-2k,j-2k+1: k >= 1) for 1<=j<=i-1, where T(m,n) := 0 if m<0 or n<0.
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6
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 1, 1, 1, 2, 3, 4, 3, 1, 1, 1, 1, 2, 3, 5, 6, 4, 1, 1, 1, 1, 2, 3, 5, 7, 7, 4, 1, 1, 1, 1, 2, 3, 5, 8, 11, 10, 5, 1, 1, 1, 1, 2, 3, 5, 8, 12, 14, 11, 5, 1, 1, 1, 1, 2, 3, 5, 8, 13
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,14
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COMMENTS
| T(i+j,j)=number of strings (s(1),...,s(m)) of nonnegative integers s(k) such that m<=i+1, s(m)=j and s(k)-s(k-1) is an odd positive integer for k=2,3,...,m.
T(i+j,j)=number of compositions of numbers <=j using up to i parts, each an odd positive integer.
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EXAMPLE
| Rows: 1; 1,1; 1,1,1; 1,1,1,1; 1,1,1,2,1; ...
T(9,6) counts the strings 3456, 1236, 1256, 1456, 036, 016, 056.
T(9,6) counts the compositions 111, 113, 131, 311, 33, 15, 51.
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CROSSREFS
| Infinitely many of the columns are (1, 1, 1, 2, 3, 5, 8, ..., Fibonacci numbers)
Essentially a reflected version of A011794.
Sequence in context: A139038 A139040 A139147 * A155050 A140356 A119963
Adjacent sequences: A055798 A055799 A055800 * A055802 A055803 A055804
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), May 28 2000
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