A138997 First differences of Frobenius numbers for 6 successive numbers A138986.

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, 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, 12, 74, 13, 13, 13, 13, 80, 14, 14, 14, 14, 86, 15, 15, 15, 15, 92, 16, 16, 16, 16, 98, 17, 17

Offset

1,5

Links

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

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

Formula

a(n) = A138986(n+1) - A138986(n).

From R. J. Mathar, Apr 20 2008: (Start)

O.g.f.: -x*(-1-x-x^2-x^3-8*x^4+2*x^9)/((x-1)^2*(x^4+x^3+x^2+x+1)^2).

a(n) = 2*a(n-5) - a(n-10). (End)

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

Mathematica

a = {}; Do[AppendTo[a, FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5, n + 6}]], {n, 1, 100}]; Differences[a]
LinearRecurrence[{0, 0, 0, 0, 2, 0, 0, 0, 0, -1}, {1, 1, 1, 1, 8, 2, 2, 2, 2, 14}, 90] (* G. C. Greubel, Feb 18 2017 *)
Differences[Table[FrobeniusNumber[Range[n, n+5]], {n, 2, 90}]] (* Harvey P. Dale, Dec 18 2023 *)

Prog

(PARI) my(x='x + O('x^90)); Vec(-x*(-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

Crossrefs

For first differences of Frobenius numbers for k successive numbers see: A005843 (k=2), A014682 (k=3), A138995 (k=4), A138996 (k=5), A138997 (k=6), A151898 (k=7), A138999 (k=8).

Cf. A028387, A037165, A079326, A138985, A138986, A138987, A138988, A138989, A138990, A138991, A138992, A138993, A138994.

Sequence in context: A136711 A037920 A388567 * A248498 A133918 A072691

Adjacent sequences: A138994 A138995 A138996 * A138998 A138999 A139000

Keyword

nonn,easy

Author

Artur Jasinski, Apr 05 2008

Status

approved