|
%I #13 Dec 22 2018 12:04:53
%S 1,1,6,2,2,10,3,3,14,4,4,18,5,5,22,6,6,26,7,7,30,8,8,34,9,9,38,10,10,
%T 42,11,11,46,12,12,50,13,13,54,14,14,58,15,15,62,16,16,66,17,17,70,18,
%U 18,74,19,19,78,20,20,82,21,21,86,22,22,90,23,23,94,24,24,98,25,25,102,26
%N First differences of Frobenius numbers for 4 successive numbers A138984.
%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="/A138995/b138995.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F a(n) = A138984(n+1) - A138984(n).
%F a(n) = 2*a(n-3) - a(n-6). - R. J. Mathar, Apr 20 2008
%F a(n) = (1/3)*x(mod(n,3))*mod(n,3)-(1/3)*n*x(mod(n,3))+(1/3)*n*x(3+mod(n,3))+x(mod(n,3))-(1/3)*mod(n,3)*x(3+mod(n,3)). - _Alexander R. Povolotsky_, Apr 20 2008
%F G.f.: -x*(2*x^5-6*x^2-x-1) / ((x-1)^2*(x^2+x+1)^2). - _Colin Barker_, Dec 13 2012
%t a = {}; Do[AppendTo[a, FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4}]], {n, 1, 100}]; Differences[a]
%t LinearRecurrence[{0, 0, 2, 0, 0, -1}, {1, 1, 6, 2, 2, 10},50] (* _G. C. Greubel_, Feb 18 2017 *)
%t Differences[Table[FrobeniusNumber[Range[n,n+3]],{n,2,100}]] (* _Harvey P. Dale_, Dec 22 2018 *)
%o (PARI) x='x+O('x^50); Vec(-x*(2*x^5-6*x^2-x-1) / ((x-1)^2*(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,easy
%O 1,3
%A _Artur Jasinski_, Apr 05 2008
|
