

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
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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 2generator semigroup <a,b> is abab.


REFERENCES

R. Froberg, C. Gottlieb and R. Haggkvist, "On numerical semigroups", Semigroup Forum, 35 (1987), 6383 (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+8n1
a(1)=47,a(2)=287,a(3)=959,a(4)=2399,a(5)=5039,a(n)=5a(n1)10a(n2) +10a(n3)5a(n4)+a(n5). [From Harvey P. Dale, Apr 25 2011]
G.f.: x*(47+52*x6*x^2+4*x^3x^4)/(1x)^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+8n1, {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, A069755A069764.
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



