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A151898
First differences of Frobenius numbers for 7 successive numbers A138987.
1
1, 1, 1, 1, 1, 9, 2, 2, 2, 2, 2, 16, 3, 3, 3, 3, 3, 23, 4, 4, 4, 4, 4, 30, 5, 5, 5, 5, 5, 37, 6, 6, 6, 6, 6, 44, 7, 7, 7, 7, 7, 51, 8, 8, 8, 8, 8, 58, 9, 9, 9, 9, 9, 65, 10, 10, 10, 10, 10, 72, 11, 11, 11, 11, 11, 79, 12, 12, 12, 12, 12, 86, 13, 13, 13, 13, 13, 93, 14, 14, 14, 14, 14, 100, 15
OFFSET
1,6
COMMENTS
First differences of Frobenius numbers for 2 successive numbers see A005843
First differences of Frobenius numbers for 3 successive numbers see A014682
First differences of Frobenius numbers for 4 successive numbers see A138995
First differences of Frobenius numbers for 5 successive numbers see A138996
First differences of Frobenius numbers for 6 successive numbers see A138997
First differences of Frobenius numbers for 7 successive numbers see A151898
First differences of Frobenius numbers for 8 successive numbers see A138999
FORMULA
a(n) = A138987(n+1)-A138987(n).
G.f.: -x*(2*x^11-9*x^5-x^4-x^3-x^2-x-1) / ((x-1)^2*(x+1)^2*(x^2-x+1)^2*(x^2+x+1)^2). [Colin Barker, Dec 13 2012]
MATHEMATICA
a = {}; Do[AppendTo[a, FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5, n + 6, n + 7}]], {n, 1, 100}]; Differences[a]
Differences[Table[FrobeniusNumber[Range[n, n+6]], {n, 2, 90}]] (* or *) LinearRecurrence[ {0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 1, 9, 2, 2, 2, 2, 2, 16}, 90] (* Harvey P. Dale, Jul 26 2024 *)
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Apr 05 2008
STATUS
approved