

A069755


Frobenius number of the numerical semigroup generated by 3 consecutive triangular numbers.


10



17, 29, 89, 125, 251, 323, 539, 659, 989, 1169, 1637, 1889, 2519, 2855, 3671, 4103, 5129, 5669, 6929, 7589, 9107, 9899, 11699, 12635, 14741, 15833, 18269, 19529, 22319, 23759, 26927, 28559, 32129, 33965, 37961, 40013, 44459, 46739, 51659
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OFFSET

2,1


COMMENTS

The Frobenius number of the 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. Any three successive triangular numbers are relatively prime, so they generate a numerical semigroup with a Frobenius number.


REFERENCES

R. Froberg, C. Gottlieb and R. Haggkvist, "On numerical semigroups", Semigroup Forum, 35 (1987), 6383 (for definition of Frobenius number).


LINKS

Harvey P. Dale, Table of n, a(n) for n = 2..1000


FORMULA

Conjecture: a(n) = (14+6*(1)^n+(3+9*(1)^n)*n+3*(5+(1)^n)*n^2+6*n^3)/8. G.f.: x^2*(x^63*x^4+9*x^2+12*x+17)/((x1)^4*(x+1)^3). [Colin Barker, Nov 22 2012]


EXAMPLE

a(2)=17 because 17 is not a nonnegative linear combination of 3, 6 and 10 but all numbers greater than 17 are.


MATHEMATICA

tri=Range[40]Range[2, 41]/2; Table[t=CoefficientList[Series[1/(1x^tri[[n]])/(1x^tri[[n+1]])/(1x^tri[[n+2]]), {x, 0, n(n+1)(n+2)}], x]; Last[Position[t, 0]1][[1]], {n, 2, 33}]  T. D. Noe, Nov 27 2006
Rest[FrobeniusNumber/@Partition[Accumulate[Range[50]], 3, 1]] (* Harvey P. Dale, Oct 04 2011 *)


CROSSREFS

Cf. A000217, A037165, A059769, A069756A069762.
Sequence in context: A154616 A196938 A225943 * A076727 A146870 A146744
Adjacent sequences: A069752 A069753 A069754 * A069756 A069757 A069758


KEYWORD

easy,nice,nonn


AUTHOR

Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 05 2002


EXTENSIONS

Corrected by T. D. Noe, Nov 27 2006


STATUS

approved



