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A073937
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a(n)=a(n-1)-a(n-2)+a(n-3)+a(n-4), a(0)=4, a(1)=1, a(2)=-1, a(3)=1.
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3
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4, 1, -1, 1, 7, 6, -1, 1, 15, 19, 4, 1, 31, 53, 27, 6, 63, 137, 107, 39, 132, 337, 351, 185, 303, 806, 1039, 721, 791, 1915, 2884, 2481, 2303, 4621, 7683, 7846, 7087, 11545, 19987, 23375, 22020, 30177, 51519, 66737, 67415, 82374, 133215, 184993, 201567, 232163, 348804
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Apart from signs, a(n) is the coefficient of A^n in the Cayley-Hamilton equation for A^n, where A is the tetramatrix ((1,1,0,0),(1,0,1,0),(1,0,0,1), (1,0,0,0)). The matrix A is related to the tetranacci numbers A000078, A001630, A073817.
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FORMULA
| G.f.: (4-3x+2x^2-x^3)/(1-x+x^2-x^3-x^4).
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MATHEMATICA
| CoefficientList[Series[(4-3*x+2*x^2-x^3)/(1-x+x^2-x^3-x^4), {x, 0, 50}], x]
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CROSSREFS
| Cf. A000078, A001630, A073817.
Sequence in context: A063928 A131299 * A074058 A088440 A203025 A057521
Adjacent sequences: A073934 A073935 A073936 * A073938 A073939 A073940
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KEYWORD
| easy,sign
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Aug 13 2002
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