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A107271
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Let M = the 3 X 3 matrix [1 1 1; 3 1 0; 2 0 0]. Perform M^n * [1 0 0] getting (1, 3, 2; 6, 6, 2; 14, 24, 12; 50, 66, 28;...) which we string together to form the sequence.
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1, 3, 2, 6, 6, 2, 14, 24, 12, 50, 66, 28, 144, 216, 100, 460, 648, 288, 1396, 2028, 920, 4344, 6216, 2792, 13352, 19248, 8688, 41288, 59304, 26704, 127296, 183168, 82576, 393040, 565056, 254592, 1212688, 1744176, 786080
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OFFSET
| 1,2
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COMMENTS
| Sequence relating to finite differences.
Taking subsets (k = 1,2,3...) of three terms: [1, 3, 2; 6, 6, 2; 14, 24, 12;...), 3 terms in the k-th subset are coefficients in a second degree equation f(x) such that the binomial transform of (k+1)-th subset = terms generated by f(x) of k-th subset. Example: Binomial transform of [14, 24, 12] = 14, 38, 74, 122...; f(x)= 6x^2 + 6x + 2. [14, 24, 12] = the 3rd subset of 3 terms, [6, 6, 2] = the second subset. Then, binomial transform of [6, 6, 2] = [6, 12, 20, 33, 42...] such that f(x) = x^2 + 3x + 2, where [1, 3, 2] is the second three term subset of A107271.
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EXAMPLE
| M^3 * [1 0 0] = [14, 24, 12].
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CROSSREFS
| Sequence in context: A125675 A072787 A189073 * A196565 A104633 A102022
Adjacent sequences: A107268 A107269 A107270 * A107272 A107273 A107274
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 15 2005
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