A138996 First differences of Frobenius numbers for 5 successive numbers A138985.

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, 42, 9, 9, 9, 47, 10, 10, 10, 52, 11, 11, 11, 57, 12, 12, 12, 62, 13, 13, 13, 67, 14, 14, 14, 72, 15, 15, 15, 77, 16, 16, 16, 82, 17, 17, 17, 87, 18, 18, 18, 92, 19, 19, 19, 97, 20, 20, 20

Offset

1,4

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

Formula

a(n) = A138985(n+1) - A138985(n).

a(n) = 2*a(n-4) - a(n-8). - R. J. Mathar, Apr 20 2008

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

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

Mathematica

a = {}; Do[AppendTo[a, FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5}]], {n, 1, 100}]; Differences[a]
LinearRecurrence[{0, 0, 0, 2, 0, 0, 0, -1}, {1, 1, 1, 7, 2, 2, 2,
  12}, 50] (* G. C. Greubel, Feb 18 2017 *)

Prog

(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

Crossrefs

Cf. A028387, A037165, A079326, A138985, A138986, A138987, A138988, A138989, A138990, A138991, A138992, A138993, A138994, A138995, A138996, A138997, A138998, A138999.

Sequence in context: A289917 A198415 A195723 * A010141 A316247 A299922

Adjacent sequences: A138993 A138994 A138995 * A138997 A138998 A138999

Keyword

nonn,easy

Author

Artur Jasinski, Apr 05 2008

Status

approved