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A138995 First differences of Frobenius numbers for 4 successive numbers A138984. 5
1, 1, 6, 2, 2, 10, 3, 3, 14, 4, 4, 18, 5, 5, 22, 6, 6, 26, 7, 7, 30, 8, 8, 34, 9, 9, 38, 10, 10, 42, 11, 11, 46, 12, 12, 50, 13, 13, 54, 14, 14, 58, 15, 15, 62, 16, 16, 66, 17, 17, 70, 18, 18, 74, 19, 19, 78, 20, 20, 82, 21, 21, 86, 22, 22, 90, 23, 23, 94, 24, 24, 98, 25, 25, 102, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

FORMULA

a(n) = A138984(n+1) - A138984(n).

a(n) = 2*a(n-3) - a(n-6). - R. J. Mathar, Apr 20 2008

a(n) = (1/3)*x(mod(n,3))*mod(n,3)-(1/3)*n*x(mod(n,3))+(1/3)*n*x(3+mod(n,3))+x(mod(n,3))-(1/3)*mod(n,3)*x(3+mod(n,3)). - Alexander R. Povolotsky, Apr 20 2008

G.f.: -x*(2*x^5-6*x^2-x-1) / ((x-1)^2*(x^2+x+1)^2). - Colin Barker, Dec 13 2012

MATHEMATICA

a = {}; Do[AppendTo[a, FrobeniusNumber[{n + 1, n + 2, n + 3, n + 4}]], {n, 1, 100}]; Differences[a]

LinearRecurrence[{0, 0, 2, 0, 0, -1}, {1, 1, 6, 2, 2, 10}, 50] (* G. C. Greubel, Feb 18 2017 *)

Differences[Table[FrobeniusNumber[Range[n, n+3]], {n, 2, 100}]] (* Harvey P. Dale, Dec 22 2018 *)

PROG

(PARI) x='x+O('x^50); Vec(-x*(2*x^5-6*x^2-x-1) / ((x-1)^2*(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: A201674 A093497 A092138 * A010133 A065280 A247672

Adjacent sequences:  A138992 A138993 A138994 * A138996 A138997 A138998

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Apr 05 2008

STATUS

approved

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Last modified November 14 04:56 EST 2019. Contains 329110 sequences. (Running on oeis4.)