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A085691
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T(n,k) is the number of triangles of side k in triangular matchstick arrangement of side n; n>=1 and k>=1.
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1
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1, 4, 1, 9, 3, 1, 16, 7, 3, 1, 25, 13, 6, 3, 1, 36, 21, 11, 6, 3, 1, 49, 31, 18, 10, 6, 3, 1, 64, 43, 27, 16, 10, 6, 3, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| {1}, {4,1}, {9, 3, 1}, {16, 7, 3, 1}, {25, 13, 6, 3, 1}
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REFERENCES
| J.H Conway and R.K Guy, The Book of Numbers,p.83.
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FORMULA
| T(n, k) = 0 if n<k; T(n, k) = (n-k+1).(n-k+2)/2 if k<= n<2.(k-1); T(n, k)= n^2 - 3.(k-1).n + (5.k-4).(k-1)/2; Row sums = A002717; T(n, 1)=A000290, T(n, 2)give A002061; T(n, 3)give A010000
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CROSSREFS
| Cf. A002717, A000290, A002061, A010000.
Sequence in context: A181859 A085383 A153265 * A055461 A104796 A132020
Adjacent sequences: A085688 A085689 A085690 * A085692 A085693 A085694
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KEYWORD
| nonn,tabl
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AUTHOR
| DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jul 18 2003
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