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.

A212240 Number of 2 X 2 matrices M with all terms in {1,...,n} and permanent(M) >= n.

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%I A212240 #26 May 20 2025 08:30:26
%S A212240 0,1,16,80,251,612,1269,2354,4021,6449,9844,14427,20458,28203,37972,
%T A212240 50073,64876,82725,104046,129222,158741,193024,232607,277956,329675,
%U A212240 388248,454353,528508,611435,703712,806121,919242,1043953,1180865
%N A212240 Number of 2 X 2 matrices M with all terms in {1,...,n} and permanent(M) >= n.
%C A212240 For a guide to related sequences, see A211795.
%F A212240 a(n) + A212151(n) = n^4.
%t A212240 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212240 (Do[If[w*x + y*z >= n, s = s + 1],
%t A212240 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212240 Map[t[#] &, Range[0, 40]]  (* A212240 *)
%t A212240 (* _Peter J. C. Moses_, Apr 13 2012 *)
%o A212240 (Python)
%o A212240 from sympy import divisor_count
%o A212240 def A212240(n): return  n**4-sum((sum(divisor_count(i+1)*divisor_count(j-i) for i in range(j>>1))<<1)+(divisor_count(j+1>>1)**2 if j&1 else 0) for j in range(1,n-1)) # _Chai Wah Wu_, Jul 26 2024
%Y A212240 Cf. A211795, A212151.
%K A212240 nonn
%O A212240 0,3
%A A212240 _Clark Kimberling_, May 07 2012
%E A212240 Offset changed to 0 by _Georg Fischer_, Feb 03 2022