This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A069764 #27 Aug 20 2025 10:57:54
%S A069764 89,773,3611,12179,33349,78889,167383,326471,595409,1027949,1695539,
%T A069764 2690843,4131581,6164689,8970799,12769039,17822153,24441941,32995019,
%U A069764 43908899,57678389,74872313,96140551,122221399,153949249,192262589,238212323,292970411,357838829
%N A069764 Frobenius number of the numerical semigroup generated by consecutive octahedral numbers.
%C A069764 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.
%H A069764 Harvey P. Dale, <a href="/A069764/b069764.txt">Table of n, a(n) for n = 2..1000</a>
%H A069764 R. Fröberg, C. Gottlieb and R. Häggkvist, <a href="https://gdz.sub.uni-goettingen.de/id/PPN362162808_0035">On numerical semigroups</a>, Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).
%H A069764 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A069764 a(n) = ((1/3)*n*(2*n^2+1)-1)*((1/3)*(n+1)*(2*(n+1)^2+1)-1)-1.
%F A069764 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
%F A069764 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
%e A069764 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.
%t A069764 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 *)
%Y A069764 Cf. A005900, A037165, A059769, A069755-A069763.
%K A069764 nonn,easy
%O A069764 2,1
%A A069764 Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 18 2002
%E A069764 More terms from _Carl Najafi_, Sep 10 2011