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Search: id:A026082
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| A026082 |
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Triangular array T read by rows: T(n,k)=C(n,k) for k=0,1,...,n for n=0,1,2,3. For n >= 4, T(n,0)=T(n,2n)=1,T(n,1)=T(n,2n-1)=n-3,T(4,2)=4,T(4,3)=3,T(4,4)=6; T(4,5)=3,T(4,6)=4; for n >= 5,T(n,k)=T(n-1,k-2)+T(n-1,k-1)+T(n-1,k) for k=2,3,...,2n-2. For n >= 4, T(n,k)=number of integer strings s(0),...,s(n) such that s(n)=n-k,s(0)=0,|s(i)-s(i-1)|=1 for i=1,2,3 and <=1 for i >= 4. |
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+0
21
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| 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 1, 4, 3, 6, 3, 4, 1, 1, 1, 2, 6, 8, 13, 12, 13, 8, 6, 2, 1, 1, 3, 9, 16, 27, 33, 38, 33, 27, 16, 9, 3, 1, 1, 4, 13, 28, 52, 76, 98, 104, 98, 76, 52, 28, 13, 4, 1, 1, 5, 18, 45, 93, 156, 226, 278, 300, 278, 226, 156, 93, 45, 18, 5, 1, 1, 6, 24, 68, 156, 294, 475, 660, 804
(list; graph; listen)
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OFFSET
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0,5
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FORMULA
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G.f.: (1-yz)^3 / [1-z(1+y+y^2)].
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EXAMPLE
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1; 1,1; 1,2,1; 1,3,3,1; 1,1,4,3,6,3,4,1,1; 1,2,6,8,13,12,13,8,6,2,1; ...
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CROSSREFS
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First differences of A024996.
Sequence in context: A129571 A034931 A090402 this_sequence A117185 A129181 A093557
Adjacent sequences: A026079 A026080 A026081 this_sequence A026083 A026084 A026085
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KEYWORD
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nonn,tabf
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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