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A185081
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Triangle T(n,k), read by rows, given by (0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
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2
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1, 0, 1, 0, 1, 2, 0, 2, 4, 3, 0, 3, 9, 10, 5, 0, 5, 18, 28, 22, 8, 0, 8, 35, 68, 74, 45, 13, 0, 13, 66, 154, 210, 177, 88, 21, 0, 21, 122, 331, 541, 574, 397, 167, 34, 0, 34, 222, 686, 1302, 1656, 1446, 850, 310, 55
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OFFSET
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0,6
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COMMENTS
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LINKS
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FORMULA
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T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) + T(n-2,k-2), for n > 2, T(0,0) = T(1,1) = T(2,1) = 1, T(1,0) = T(2,0) = 0, T(2,2) = 2.
G.f.: (-1 + x^2*y + x + x^2)/(-1 + x^2*y + x + x^2 + x*y + x^2*y^2). - R. J. Mathar, Aug 11 2015
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 1, 2;
0, 2, 4, 3;
0, 3, 9, 10, 5;
0, 5, 18, 28, 22, 8;
0, 8, 35, 68, 74, 45, 13;
1;
1, 2;
2, 4, 3;
3, 9, 10, 5;
5, 18, 28, 22, 8;
8, 35, 68, 74, 45, 13; (End)
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MATHEMATICA
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nmax = 9; T[n_, n_] := Fibonacci[n+1]; T[_, 0] = 0; T[n_, 1] := Fibonacci[n]; T[n_, k_] /; 1 < k < n := T[n, k] = T[n - 1, k] + T[n - 1, k - 1] + T[n - 2, k] + T[n - 2, k - 1] + T[n - 2, k - 2]; T[_, _] = 0;
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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