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Search: id:A109128
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| A109128 |
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Triangle read by rows: T(n,k) = T(n-1,k-1) + T(n-1,k) + 1 for 0<k<n, T(n,0) = T(n,n) = 1. |
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+0
10
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| 1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 11, 7, 1, 1, 9, 19, 19, 9, 1, 1, 11, 29, 39, 29, 11, 1, 1, 13, 41, 69, 69, 41, 13, 1, 1, 15, 55, 111, 139, 111, 55, 15, 1, 1, 17, 71, 167, 251, 251, 167, 71, 17, 1, 1, 19, 89, 239, 419, 503, 419, 239, 89, 19, 1, 1, 21, 109, 329, 659, 923, 923
(list; table; graph; listen)
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OFFSET
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1,5
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LINKS
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Index entries for triangles and arrays related to Pascal's triangle
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FORMULA
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T(n,k) = 2*binomial(n,k) - 1. - David W. Cantrell (DWCantrell(AT)sigmaxi.net), Sep 30 2007
Sum of n-th row = 2^(n+1) - (n+1) = A000325(n+1);
T(n,1) = 2*n - 1 = A005408(n+1) for n>0;
T(n,2) = n^2 + n - 1 = A028387(n-2) for n>1.
T(n,k)=if(k<=n, sum{j=0..n-k, C(n-k,j)C(k,j)(2-0^j)},0) - Paul Barry (pbarry(AT)wit.ie), Apr 27 2006
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CROSSREFS
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Cf. A007318.
Sequence in context: A134398 A026615 A026681 this_sequence A113245 A103450 A128254
Adjacent sequences: A109125 A109126 A109127 this_sequence A109129 A109130 A109131
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KEYWORD
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nonn,tabl
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 20 2005
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