cp's OEIS Frontend

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.

A358035 a(n) = (8*n^3 + 12*n^2 + 4*n - 9)/3.

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%I A358035 #25 Nov 20 2022 19:18:21
%S A358035 5,37,109,237,437,725,1117,1629,2277,3077,4045,5197,6549,8117,9917,
%T A358035 11965,14277,16869,19757,22957,26485,30357,34589,39197,44197,49605,
%U A358035 55437,61709,68437,75637,83325,91517,100229,109477,119277,129645,140597,152149,164317
%N A358035 a(n) = (8*n^3 + 12*n^2 + 4*n - 9)/3.
%C A358035 Conjecture: a(n) is the disorder number of the Aztec diamond of size n.
%D A358035 G. E. Andrews and K. Eriksson, Integer Partitions, Cambridge University Press, 2004.
%H A358035 Sela Fried, <a href="https://arxiv.org/abs/2208.03788">The disorder number of a graph</a>, arXiv:2208.03788 [math.CO], 2022.
%H A358035 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A358035 G.f.: x*(5 + 17*x - 9*x^2 + 3*x^3)/(1 - x)^4. - _Stefano Spezia_, Oct 26 2022
%t A358035 Table[(8n^3+12n^2+4n-9)/3,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{5,37,109,237},40] (* _Harvey P. Dale_, Nov 20 2022 *)
%o A358035 (Python)
%o A358035 def A358035(n): return n*(n*((n<<3) + 12) + 4)//3 - 3 # _Chai Wah Wu_, Oct 31 2022
%Y A358035 Cf. A354528.
%K A358035 nonn,easy
%O A358035 1,1
%A A358035 _Sela Fried_, Oct 26 2022