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

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 (0,0,0,0,2,0,0,0,0,-1).

Formula

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

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

a(n) = 2*a(n-5) - a(n-10). - R. J. Mathar, Apr 20 2008

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}, 50] (* G. C. Greubel, Feb 18 2017 *)
Differences[Table[FrobeniusNumber[Range[n, n+5]], {n, 2, 90}]] (* Harvey P. Dale, Dec 18 2023 *)

Prog

(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

Crossrefs

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

Sequence in context: A176153 A136711 A037920 * A248498 A133918 A072691

Adjacent sequences: A138994 A138995 A138996 * A138998 A138999 A139000

Keyword

nonn

Author

Artur Jasinski, Apr 05 2008

Status

approved