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
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
KEYWORD
easy,nonn
AUTHOR
Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 09 2002
STATUS
approved