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A138997
First differences of Frobenius numbers for 6 successive numbers A138986.
5
1, 1, 1, 1, 8, 2, 2, 2, 2, 14, 3, 3, 3, 3, 20, 4, 4, 4, 4, 26, 5, 5, 5, 5, 32, 6, 6, 6, 6, 38, 7, 7, 7, 7, 44, 8, 8, 8, 8, 50, 9, 9, 9, 9, 56, 10, 10, 10, 10, 62, 11, 11, 11, 11, 68, 12, 12, 12, 12, 74, 13, 13, 13, 13, 80, 14, 14, 14, 14, 86, 15, 15, 15, 15, 92, 16, 16, 16, 16, 98, 17, 17
OFFSET
1,5
COMMENTS
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
FORMULA
a(n) = A138986(n+1) - A138986(n).
O.g.f.= -(-1-x-x^2-x^3-8*x^4+2*x^9)/((x-1)^2*(x^4+x^3+x^2+x+1)^2). - R. J. Mathar, Apr 20 2008
a(n) = 2*a(n-5) - a(n-10). - R. J. Mathar, Apr 20 2008
a(n)= (1/5)*n*x(5+mod(n,5))-(1/5)*mod(n,5)*x(5+mod(n,5))+x(mod(n,5))-(1/5)*n*x(mod(n,5))+(1/5) *mod(n,5)*x(mod(n,5)). - Alexander R. Povolotsky, Apr 20 2008
MATHEMATICA
a = {}; Do[AppendTo[a, FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5, n + 6}]], {n, 1, 100}]; Differences[a]
LinearRecurrence[{0, 0, 0, 0, 2, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 8, 2,
2, 2, 2, 14}, 50] (* G. C. Greubel, Feb 18 2017 *)
Differences[Table[FrobeniusNumber[Range[n, n+5]], {n, 2, 90}]] (* Harvey P. Dale, Dec 18 2023 *)
PROG
(PARI) x='x + O('x^50); Vec(-(-1-x-x^2-x^3-8*x^4+2*x^9)/((x-1)^2*(x^4+x^3+x^2+x+1)^2)) \\ G. C. Greubel, Feb 18 2017
KEYWORD
nonn
AUTHOR
Artur Jasinski, Apr 05 2008
STATUS
approved