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%I #13 Feb 10 2021 08:12:05
%S 47,287,959,2399,5039,9407,16127,25919,39599,58079,82367,113567,
%T 152879,201599,261119,332927,418607,519839,638399,776159,935087,
%U 1117247,1324799,1559999,1825199,2122847
%N Frobenius number of the numerical semigroup generated by consecutive centered square numbers.
%C 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.
%D R. Fröberg, C. Gottlieb and R. Häggkvist, "On numerical semigroups", Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F a(n) = 4n^4+16n^3+20n^2+8n-1
%F 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]
%F G.f.: x*(47+52*x-6*x^2+4*x^3-x^4)/(1-x)^5. [Colin Barker, Feb 14 2012]
%e a(1)=47 because 47 is not a nonnegative linear combination of 5 and 13, but all integers greater than 47 are.
%t 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 *)
%Y Cf. A001844, A037165, A059769, A069755-A069764.
%K easy,nonn
%O 1,1
%A Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 09 2002
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