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Search: id:A100329
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| A100329 |
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a(n)=-a(n-1)-a(n-2)-a(n-3)+a(n-4), a(0)=0,a(1)=1,a(2)=-1,a(3)=0. |
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+0
1
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| 0, 1, -1, 0, 0, 2, -3, 1, 0, 4, -8, 5, -1, 8, -20, 18, -7, 17, -48, 56, -32, 41, -113, 160, -120, 114, -267, 433, -400, 348, -648, 1133, -1233, 1096, -1644, 2914, -3599, 3425, -4384, 7472, -10112, 10449, -12193, 19328, -27696, 31010, -34835, 50849, -74720, 89716, -100680
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Reflected tetranacci numbers: a(n)=A000078(-n).
Let Q(n) = A000078, then a(n) = (-1)^(n+1)(Q(n)^3 - 2Q(n-1)Q(n)Q(n+1) + Q(n-2)Q(n+1)^2 + Q(n-1)^2Q(n+2) - Qn(-2)Q(n)Q(n+2))
derived from powers of the inverse of a generalized Fibonacci matrix
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FORMULA
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G.f.: x/(1+x+x^2+x^3-x^4).
a(n) = term (1,4) in the 4x4 matrix [1,1,0,0; 1,0,1,0; 1,0,0,1; 1,0,0,0]^(-n). - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 12 2008
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MAPLE
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a := n -> (Matrix([[1, 1, 0, 0], [1, 0, 1, 0], [1, 0, 0, 1], [1, 0, 0, 0]])^(-n))[1, 4]; seq ((a(n)), n=0..50); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 12 2008
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MATHEMATICA
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CoefficientList[Series[x/(1+x+x^2+x^3-x^4), {x, 0, 50}], x]
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CROSSREFS
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Cf. Tribonacci A000073, reflected tribonacci A057597.
Sequence in context: A137396 A115352 A038554 this_sequence A081247 A005210 A048994
Adjacent sequences: A100326 A100327 A100328 this_sequence A100330 A100331 A100332
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KEYWORD
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sign
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AUTHOR
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Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) Nov 16 2004
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