login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A069764 Frobenius number of the numerical semigroup generated by consecutive octahedral numbers. 9
89, 773, 3611, 12179, 33349, 78889, 167383, 326471, 595409, 1027949, 1695539, 2690843, 4131581, 6164689, 8970799, 12769039, 17822153, 24441941, 32995019, 43908899, 57678389, 74872313, 96140551, 122221399, 153949249, 192262589, 238212323 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

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 octahedral numbers are relatively prime, they generate a numerical semigroup with a Frobenius number. The Frobenius number of a 2-generated semigroup <a,b> has the formula 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

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

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

FORMULA

a(n)=((1/3)n(2n^2+1)-1)((1/3)(n+1)(2(n+1)^2+1)-1)-1.

G.f.: x^2*(89+150*x+69*x^2+20*x^3-13*x^4+6*x^5-x^6)/(1-x)^7. [Colin Barker, Feb 12 2012]

a(2)=89, a(3)=773, a(4)=3611, a(5)=12179, a(6)=33349, a(7)=78889, a(8)=167383, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+ 21*a(n-5)- 7*a(n-6)+a(n-7). - Harvey P. Dale, Nov 19 2015

EXAMPLE

a(2)=89 because 89 is not a nonnegative linear combination of 6 and 19 (the second and third octahedral numbers), but all integers greater than 89 are.

MATHEMATICA

FrobeniusNumber/@Partition[Rest[Table[(n(2n^2+1))/3, {n, 30}]], 2, 1] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {89, 773, 3611, 12179, 33349, 78889, 167383}, 30] (* Harvey P. Dale, Nov 19 2015 *)

CROSSREFS

Cf. A005900, A037165, A059769, A069755-A069763.

Sequence in context: A142566 A063654 A308801 * A053580 A239719 A290314

Adjacent sequences:  A069761 A069762 A069763 * A069765 A069766 A069767

KEYWORD

nonn

AUTHOR

Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 18 2002

EXTENSIONS

More terms from Carl Najafi, Sep 10 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 9 01:35 EDT 2020. Contains 336310 sequences. (Running on oeis4.)