A151898 First differences of Frobenius numbers for 7 successive numbers A138987.

1, 1, 1, 1, 1, 9, 2, 2, 2, 2, 2, 16, 3, 3, 3, 3, 3, 23, 4, 4, 4, 4, 4, 30, 5, 5, 5, 5, 5, 37, 6, 6, 6, 6, 6, 44, 7, 7, 7, 7, 7, 51, 8, 8, 8, 8, 8, 58, 9, 9, 9, 9, 9, 65, 10, 10, 10, 10, 10, 72, 11, 11, 11, 11, 11, 79, 12, 12, 12, 12, 12, 86, 13, 13, 13, 13, 13, 93, 14, 14, 14, 14, 14, 100, 15

Offset: 1

Author

Artur Jasinski, Apr 05 2008

Keywords

• nonn
• easy

Comments

First differences of Frobenius numbers for 2 successive numbers see A005843

First differences of Frobenius numbers for 3 successive numbers see A014682

First differences of Frobenius numbers for 4 successive numbers see A138995

First differences of Frobenius numbers for 5 successive numbers see A138996

First differences of Frobenius numbers for 6 successive numbers see A138997

First differences of Frobenius numbers for 7 successive numbers see A151898

First differences of Frobenius numbers for 8 successive numbers see A138999

Links

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

Crossrefs

Cf. A028387, A037165, A079326, A138985, A138986, A138987, A138988.

Cf. A138989, A138990, A138991, A138992, A138993, A138994.

Cf. A005843, A014682, A138995, A138996, A138997, A138999.

Programs

Mathematica

a = {}; Do[AppendTo[a, FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4, n + 5, n + 6, n + 7}]], {n, 1, 100}]; Differences[a]
Differences[Table[FrobeniusNumber[Range[n,n+6]],{n,2,90}]] (* or *) LinearRecurrence[ {0,0,0,0,0,2,0,0,0,0,0,-1},{1,1,1,1,1,9,2,2,2,2,2,16},90] (* Harvey P. Dale, Jul 26 2024 *)

Formula

a(n) = A138987(n+1)-A138987(n).

G.f.: -x*(2*x^11-9*x^5-x^4-x^3-x^2-x-1) / ((x-1)^2*(x+1)^2*(x^2-x+1)^2*(x^2+x+1)^2). [Colin Barker, Dec 13 2012]