A069760 Frobenius number of the numerical semigroup generated by consecutive centered square numbers.

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

Offset: 1

Author

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

Keywords

• easy
• nonn

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 is ab-a-b.

Examples

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

Links

• R. Fröberg, C. Gottlieb and R. Häggkvist, On numerical semigroups, Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

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

Programs

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 *)

Formula

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

a(n) = 5*a(n-1)-10*a(n-2) +10*a(n-3)-5*a(n-4)+a(n-5). - 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