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A073133
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Table by antidiagonals of T(n,k)=n*T(n,k-1)+T(n,k-2) starting with T(n,1)=1.
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10
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1, 1, 1, 1, 2, 2, 1, 3, 5, 3, 1, 4, 10, 12, 5, 1, 5, 17, 33, 29, 8, 1, 6, 26, 72, 109, 70, 13, 1, 7, 37, 135, 305, 360, 169, 21, 1, 8, 50, 228, 701, 1292, 1189, 408, 34, 1, 9, 65, 357, 1405, 3640, 5473, 3927, 985, 55, 1, 10, 82, 528, 2549, 8658, 18901, 23184, 12970
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Columns of the array are generated from Fibonacci polynomials f(x). They are: (1), (x), (x^2 + 1), (x^3 + 2x), (x^4 + 3x^2 + 1), (x^5 + 4x^3 + 3x), (x^6 + 5x^4 + 6x^2 +1),... If column headings start 0, 1, 2... then the terms in the n-th column are generated from the n-th degree Fibonacci polynomial. For example, column 5 (8, 70, 360,...) is generated from f(x), x = 1,2,3...; fifth degree polynomial x^5 + 4x^3 + 3x; e.g. f(2) = 70 = 2^5 + 4*8 + 3*2. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 02 2006
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FORMULA
| T(n, k) =A073134(n, k)+2*A073135(n, k-2) =sum_j{0<=j<k) abs(A049310(k-1, j)*n^j)
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EXAMPLE
| Table begins:
1, 1, 2, 3, 5, 8, 13, ...
1, 2, 5, 12, 29, 70, 169, ...
1, 3, 10, 33, 109, 360, 1189, ...
1, 4, 17, 72, 305, 1292, 5473, ... etc.
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CROSSREFS
| Rows include (with some gaps) A000045, A000129, A006190, A001076, A052918, A005668, A054413, A041025, A041041, A049666, A041061, A041085 etc. Columns include A000012, A000027, A002522, A054602, A057721, etc.
Different from A081572.
Sequence in context: A140767 A060850 A038137 * A106179 A081572 A144287
Adjacent sequences: A073130 A073131 A073132 * A073134 A073135 A073136
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jul 16 2002
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