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Search: id:A125250
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| A125250 |
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Array, read by antidiagonals, where A(1,1) = A(2,2) = 1, A(1,2) = A(2,1) = 0, A(n,k) = 0 if n<1 or k<1, otherwise A(n,k) = A(n-2,k-2) + A(n-1,k-2) + A(n-2,k-1) + A(n-1,k-1). |
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1
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| 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 5, 1, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 3, 11, 3, 0, 0, 0, 0, 0, 0, 1, 13, 13, 1, 0, 0, 0, 0, 0, 0, 0, 9, 26, 9, 0, 0, 0, 0, 0, 0, 0, 0, 4, 32, 32, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 26, 63, 26, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 80, 80
(list; table; graph; listen)
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OFFSET
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1,13
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COMMENT
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It appears that the main diagonal (1,1,2,5,11,...) is A05186 (Whitney number of level n of the lattice of the ideals of the fence of size 2 n) that the diagonals (0,1,2,5,13,...) adjacent to the main diagonal are A110320 (Number of blocks in all RNA secondary structures with n nodes), and that the n-th antidiagonal sum = A094686(n-1) (a Fibonacci convolution). The n-th row sum = A002605(n).
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FORMULA
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A(1,1) = A(2,2) = 1, A(1,2) = A(2,1) = 0, A(n,k) = 0 if n<1 or k<1, otherwise A(n,k) = A(n-2,k-2) + A(n-1,k-2) + A(n-2,k-1) + A(n-1,k-1)
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EXAMPLE
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Example:
Array starts as
1 0 0 0 0 0 0 ...
0 1 1 0 0 0 0 ...
0 1 2 2 1 0 0 ...
...
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PROGRAM
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(PARI) A=matrix(22, 22); A[1, 1]=1; A[2, 2]=1; A[2, 1]=0; A[1, 2]=0; A[3, 2]=1; A[2, 3]=1; for(n=3, 22, for(k=3, 22, A[n, k]=A[n-2, k-2]+A[n-1, k-2]+A[n-2, k-1]+A[n-1, k-1])); for(n=1, 22, for(i=1, n, print1(A[n-i+1, i], ", ")))
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CROSSREFS
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Cf. A051286, A110320, A002605.
Sequence in context: A051907 A093569 A073091 this_sequence A048113 A028961 A110177
Adjacent sequences: A125247 A125248 A125249 this_sequence A125251 A125252 A125253
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KEYWORD
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nonn,tabl
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AUTHOR
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Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Jan 15 2007
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