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A138996
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First differences of Frobenius numbers for 5 successive numbers A138985.
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5
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1, 1, 1, 7, 2, 2, 2, 12, 3, 3, 3, 17, 4, 4, 4, 22, 5, 5, 5, 27, 6, 6, 6, 32, 7, 7, 7, 37, 8, 8, 8, 42, 9, 9, 9, 47, 10, 10, 10, 52, 11, 11, 11, 57, 12, 12, 12, 62, 13, 13, 13, 67, 14, 14, 14, 72, 15, 15, 15, 77, 16, 16, 16, 82, 17, 17, 17, 87, 18, 18, 18, 92, 19, 19, 19, 97, 20, 20, 20
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refs;
listen;
history;
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OFFSET
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1,4
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COMMENTS
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For first differences of Frobenius numbers for 2 successive numbers see A005843
For first differences of Frobenius numbers for 3 successive numbers see A014682
For first differences of Frobenius numbers for 4 successive numbers see A138995
For first differences of Frobenius numbers for 5 successive numbers see A138996
For first differences of Frobenius numbers for 6 successive numbers see A138997
For first differences of Frobenius numbers for 7 successive numbers see A138998
For first differences of Frobenius numbers for 8 successive numbers see A138999
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LINKS
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FORMULA
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a(n) = 2*a(n-4) - a(n-8). - R. J. Mathar, Apr 20 2008
a(n) = -(1/4)*mod(n,4)*x(4+mod(n,4))+(1/4)*n*x(4+mod(n,4))+x(mod(n,4))-(1/4)*n*x(mod(n,4))+(1/4)*mod(n,4)*x(mod(n,4)). - Alexander R. Povolotsky, Apr 20 2008
G.f.: -x*(2*x^7-7*x^3-x^2-x-1) / ((x-1)^2*(x+1)^2*(x^2+1)^2). - Colin Barker, Dec 13 2012
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MATHEMATICA
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a = {}; Do[AppendTo[a, FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5}]], {n, 1, 100}]; Differences[a]
LinearRecurrence[{0, 0, 0, 2, 0, 0, 0, -1}, {1, 1, 1, 7, 2, 2, 2,
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PROG
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(PARI) x='x+O('x^50); Vec(-x*(2*x^7-7*x^3-x^2-x-1) / ((x-1)^2*(x+1)^2*(x^2+1)^2)) \\ G. C. Greubel, Feb 18 2017
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CROSSREFS
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Cf. A028387, A037165, A079326, A138985, A138986, A138987, A138988, A138989, A138990, A138991, A138992, A138993, A138994, A138995, A138996, A138997, A138998, A138999.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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