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A118007
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Triangle, diagonals generated from Lucas polynomials.
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1
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2, 3, 2, 7, 4, 2, 18, 14, 5, 2, 47, 52, 23, 6, 2, 123, 194, 110, 34, 7, 2, 322, 724, 527, 198, 47, 8, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Leftmost column = alternate Lucas numbers: (2, 3, 7, 18...), given the Lucas sequence starting (2, 1, 3, 4, 7, 11, l8,...). Refer to A084534 for a variation of the Lucas polynomials.
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REFERENCES
| Jay Kappraff, "Beyond Measure, A Guided tour Through Nature, Myth and Number", World Scientific, 2002, p. 485 (Table 22.6b).
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FORMULA
| Diagonals are sequences as f(x), x=1,2,3; Lucas polynomials in the format: (2); (x + 2); (x^2 + 4x + 2); (x^3 + 6x^2 + 9x + 2); (x^4 + 8x^3 + 20x^2 + 16x + 2); (x^5 + 10x^4 + 35x^3 + 50x^2 + 25x + 2);... Diagonals of the triangle are binomial transforms of A118008 rows.
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EXAMPLE
| First few rows of the triangle are:
2;
3, 2;
7, 4, 2;
18, 14, 5, 2;
47, 52, 23, 6, 2;
123, 194, 110, 34, 7, 2;
...
For example, 4-th diagonal from the right (18, 52, 110...) = f(x), x=1,2,3...: x^3 + 6x^2 + 9x + 2.
(18, 52, 110...) = binomial transform of 4-th row of A118008: (18, 34, 24, 6).
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CROSSREFS
| Cf. A084534, A118008.
Sequence in context: A051886 A180916 A205687 * A195401 A158747 A122697
Adjacent sequences: A118004 A118005 A118006 * A118008 A118009 A118010
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 09 2006
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