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A027926
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Triangular array T read by rows: T(n,0)=T(n,2n)=1 for n >= 0; T(n,1)=1 for n >= 1; T(n,k)=T(n-1,k-2)+T(n-1,k-1) for k=2,3,...,2n-1, n >= 2.
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23
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1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 3, 4, 3, 1, 1, 1, 2, 3, 5, 7, 7, 4, 1, 1, 1, 2, 3, 5, 8, 12, 14, 11, 5, 1, 1, 1, 2, 3, 5, 8, 13, 20, 26, 25, 16, 6, 1, 1, 1, 2, 3, 5, 8, 13, 21, 33, 46, 51, 41, 22, 7, 1, 1, 1, 2, 3, 5, 8, 13, 21, 34, 54, 79, 97, 92, 63, 29
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OFFSET
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0,7
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COMMENTS
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T(n,k) = number of strings s(0),...,s(n) such that s(0)=0, s(n)=n-k and for 1<=i<=n, s(i)=s(i-1)+d, with d in {0,1,2} if i=0, in {0,2} if s(i)=2i, in {0,1,2} if s(i)=2i-1, in {0,1} if 0<=s(i)<=2i-2.
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LINKS
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Table of n, a(n) for n=0..78.
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FORMULA
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T(n, k)=sum(binomial(n-j, 2n-k-2j), j=0..floor[(2n-k+1)/2]). - Len Smiley (smiley(AT)math.uaa.alaska.edu), Oct 21 2001
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EXAMPLE
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1;
1 1 1;
1 1 2 2 1;
1 1 2 3 4 3 1;
1 1 2 3 5 7 7 4 1;
1 1 2 3 5 8 12 14 11 5 1;
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PROG
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(PARI) T(n, k)=if(k<0|k>2*n, 0, sum(j=max(0, k-n), k\2, binomial(k-j, j)))
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CROSSREFS
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Many columns of T are A000045 (Fibonacci sequence), also in T: A001924, A004006, A000071, A000124, A014162, A014166, A027927-A027933.
Sequence in context: A047070 A071127 A029381 * A114730 A031282 A085685
Adjacent sequences: A027923 A027924 A027925 * A027927 A027928 A027929
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KEYWORD
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nonn,tabf
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AUTHOR
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Clark Kimberling
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EXTENSIONS
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Incorporates comments from Michael Somos
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STATUS
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approved
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