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Search: id:A055794
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| A055794 |
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Array T read by rows: T(i,0)=1 for i >= 0; T(i,i)=0 for i=0,1,2,3; T(i,i)=0 for i >= 4; T(i,j)=T(i-1,j)+T(i-2,j-1) for 1<=j<=i-1. |
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+0
6
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| 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 4, 2, 0, 1, 5, 7, 4, 1, 0, 1, 6, 11, 8, 3, 0, 0, 1, 7, 16, 15, 7, 1, 0, 0, 1, 8, 22, 26, 15, 4, 0, 0, 0, 1, 9, 29, 42, 30, 11, 1, 0, 0, 0, 1, 10, 37, 64, 56, 26, 5, 0, 0, 0, 0, 1, 11, 46, 93, 98, 56, 16, 1, 0, 0, 0, 0, 1, 12
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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T(i+j,j)=number of strings (s(1),...,s(i+1)) of nonnegative integers s(k) such that 0<=s(k)-s(k-1)<=1 for k=2,3,...,i+1, and s(i+1)=j.
T(i+j,j)=number of compositions of j consisting of i parts, all of in {0,1}.
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EXAMPLE
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Rows: 1; 1,1; 1,2,1; 1,3,2,1; 1,4,4,2,0; ...
T(7,4) counts the strings 3334, 3344, 3444, 2234, 2334, 2344, 1234.
T(7,4) counts the compositions 001, 010, 100, 011, 101, 110, 111.
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CROSSREFS
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Row sums: A000032 (Lucas numbers, 1, 2, 4, 7, 11, 18, ...).
T(2n, n)=A000125(n) (Cake numbers, 1, 2, 4, 8, 15, 26, ...).
T(2n+2, n)=A027660(n).
Sequence in context: A025474 A136575 A077592 this_sequence A092905 A052511 A052509
Adjacent sequences: A055791 A055792 A055793 this_sequence A055795 A055796 A055797
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), May 28 2000
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