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 A087908 #37 Sep 08 2022 08:45:11
%S A087908 -1,3,17,47,99,179,293,447,647,899,1209,1583,2027,2547,3149,3839,4623,
%T A087908 5507,6497,7599,8819,10163,11637,13247,14999,16899,18953,21167,23547,
%U A087908 26099
%N A087908 Largest integer not expressible as a nonnegative linear combination of n and n^2 + 1.
%H A087908 Vincenzo Librandi, <a href="/A087908/b087908.txt">Table of n, a(n) for n = 1..10000</a>
%H A087908 M. Beck and S. Zack, <a href="https://arxiv.org/abs/math/0305420">Refined upper bounds for the Diophantine problem of Frobenius</a>, arXiv:math/0305420 [math.NT], 2003-2005.
%H A087908 A. Brauer and J.E. Shockley, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002179997">On a Problem of Frobenius</a>, J. reine angew. Math. 211(1962), 215-220.
%H A087908 Robert W. Owens, <a href="http://www.jstor.org/stable/3219081">An Algorithm to Solve the Frobenius Problem</a>, Math. Mag. 76(2003), 264-275.
%H A087908 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A087908 a(n) = n^3 - n^2 - 1. [This follows from the well-known fact that the largest integer not expressible as a nonnegative linear combination of a and b is the number ab-a-b. - Matthias Beck (beck(AT)math.sfsu.edu), Sep 22 2005]
%F A087908 a(1)=-1, a(2)=3, a(3)=17, a(4)=47; for n>4, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Harvey P. Dale_, Jul 19 2011
%F A087908 G.f.: x*(x*((x-1)*x+7)-1)/(x-1)^4. - _Harvey P. Dale_, Jul 19 2011
%F A087908 a(n) = (n-1)*A064808(n) - n*A064808(n-1). [_Bruno Berselli_, May 19 2015]
%e A087908 For n=2, we have to consider nonnegative linear combinations of 2 and 5. Now 3 is not such a combination, but 4=2*2 and 5=1*5 and any positive integer greater than 3 is of the form 2a+b where a and b are nonnegative integers with b equal to 4 or 5. Therefore a(2)=3.
%p A087908 with (combinat):seq(n^3-fibonacci(3, n), n=1..29); # _Zerinvary Lajos_, May 25 2008
%t A087908 Table[n^3-n^2-1,{n,100}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 15 2011 *)
%t A087908 LinearRecurrence[{4,-6,4,-1},{-1,3,17,47},100] (* _Harvey P. Dale_, Jul 19 2011 *)
%o A087908 (Magma) [n^3-n^2-1: n in [1..35]]; // _Vincenzo Librandi_, Jul 20 2011
%o A087908 (PARI) a(n)=n^3-n^2-1 \\ _Charles R Greathouse IV_, Aug 01 2011
%Y A087908 Cf. A064808.
%K A087908 sign,easy
%O A087908 1,2
%A A087908 _John W. Layman_, Oct 15 2003