|
%I #11 Feb 18 2017 16:34:14
%S 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,
%T 42,9,9,9,47,10,10,10,52,11,11,11,57,12,12,12,62,13,13,13,67,14,14,14,
%U 72,15,15,15,77,16,16,16,82,17,17,17,87,18,18,18,92,19,19,19,97,20,20,20
%N First differences of Frobenius numbers for 5 successive numbers A138985.
%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="/A138996/b138996.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F a(n) = A138985(n+1) - A138985(n).
%F a(n) = 2*a(n-4) - a(n-8). - R. J. Mathar, Apr 20 2008
%F 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
%F 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
%t a = {}; Do[AppendTo[a, FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5}]], {n, 1, 100}]; Differences[a]
%t LinearRecurrence[{0, 0, 0, 2, 0, 0, 0, -1}, {1, 1, 1, 7, 2, 2, 2,
%t 12}, 50] (* _G. C. Greubel_, Feb 18 2017 *)
%o (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
%Y Cf. A028387, A037165, A079326, A138985, A138986, A138987, A138988, A138989, A138990, A138991, A138992, A138993, A138994, A138995, A138996, A138997, A138998, A138999.
%K nonn,easy
%O 1,4
%A _Artur Jasinski_, Apr 05 2008
|
