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A069760 Frobenius number of the numerical semigroup generated by consecutive centered square numbers. 0
47, 287, 959, 2399, 5039, 9407, 16127, 25919, 39599, 58079, 82367, 113567, 152879, 201599, 261119, 332927, 418607, 519839, 638399, 776159, 935087, 1117247, 1324799, 1559999, 1825199, 2122847 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The Frobenius number of a numerical semigroup generated by relatively prime integers a_1,...,a_n is the largest positive integer that is not a nonnegative linear combination of a_1,...,a_n. Since consecutive centered squares are relatively prime, they generate a numerical semigroup with a Frobenius number. The Frobenius number of a 2-generator semigroup <a,b> is ab-a-b.

REFERENCES

R. Froberg, C. Gottlieb and R. Haggkvist, "On numerical semigroups", Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).

LINKS

Table of n, a(n) for n=1..26.

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

FORMULA

a(n) = 4n^4+16n^3+20n^2+8n-1

a(1)=47,a(2)=287,a(3)=959,a(4)=2399,a(5)=5039,a(n)=5a(n-1)-10a(n-2) +10a(n-3)-5a(n-4)+a(n-5). [From Harvey P. Dale, Apr 25 2011]

G.f.: x*(47+52*x-6*x^2+4*x^3-x^4)/(1-x)^5. [Colin Barker, Feb 14 2012]

EXAMPLE

a(1)=47 because 47 is not a nonnegative linear combination of 5 and 13, but all integers greater than 47 are.

MATHEMATICA

Table[4n^4+16n^3+20n^2+8n-1, {n, 30}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {47, 287, 959, 2399, 5039}, 30] (* Harvey P. Dale, Apr 25 2011 *)

CROSSREFS

Cf. A001844, A037165, A059769, A069755-A069764.

Sequence in context: A142164 A201545 A142774 * A140043 A074774 A107611

Adjacent sequences:  A069757 A069758 A069759 * A069761 A069762 A069763

KEYWORD

easy,nonn

AUTHOR

Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 09 2002

STATUS

approved

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)