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%I #8 Dec 18 2023 15:02:02
%S 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,
%T 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,
%U 12,74,13,13,13,13,80,14,14,14,14,86,15,15,15,15,92,16,16,16,16,98,17,17
%N First differences of Frobenius numbers for 6 successive numbers A138986.
%C For first differences of Frobenius numbers for 2 successive numbers see A005843
%C For first differences of Frobenius numbers for 3 successive numbers see A014682
%C For first differences of Frobenius numbers for 4 successive numbers see A138995
%C For first differences of Frobenius numbers for 5 successive numbers see A138996
%C For first differences of Frobenius numbers for 6 successive numbers see A138997
%C For first differences of Frobenius numbers for 7 successive numbers see A138998
%C For first differences of Frobenius numbers for 8 successive numbers see A138999
%H G. C. Greubel, <a href="/A138997/b138997.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,2,0,0,0,0,-1).
%F a(n) = A138986(n+1) - A138986(n).
%F 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
%F a(n) = 2*a(n-5) - a(n-10). - R. J. Mathar, Apr 20 2008
%F 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
%t a = {}; Do[AppendTo[a, FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5, n + 6}]], {n, 1, 100}]; Differences[a]
%t LinearRecurrence[{0, 0, 0, 0, 2, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 8, 2,
%t 2, 2, 2, 14}, 50] (* _G. C. Greubel_, Feb 18 2017 *)
%t Differences[Table[FrobeniusNumber[Range[n,n+5]],{n,2,90}]] (* _Harvey P. Dale_, Dec 18 2023 *)
%o (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
%Y Cf. A028387, A037165, A079326, A138985, A138986, A138987, A138988, A138989, A138990, A138991, A138992, A138993, A138994, A138995, A138996, A138997, A138998, A138999.
%K nonn
%O 1,5
%A _Artur Jasinski_, Apr 05 2008
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