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A212151 Number of 2 X 2 matrices M of positive integers such that permanent(M) < n.

%I A212151 #32 Jul 26 2024 10:21:28
%S A212151 0,0,0,1,5,13,27,47,75,112,156,214,278,358,444,552,660,796,930,1099,
%T A212151 1259,1457,1649,1885,2101,2377,2623,2933,3221,3569,3879,4279,4623,
%U A212151 5056,5452,5926,6334,6878,7328,7892,8404,9018,9540,10228,10788,11504,12142,12898
%N A212151 Number of 2 X 2 matrices M of positive integers such that permanent(M) < n.
%C A212151 For a guide to related sequences, see A211795.
%H A212151 Robert Israel, <a href="/A212151/b212151.txt">Table of n, a(n) for n = 0..10000</a>
%F A212151 a(n) + A212240(n) = n^4.
%F A212151 a(n) = Sum_{k=1..n-1} Sum_{i=1..n-1} d(k) * floor((n-k-1)/i), where d(k) is the number of divisors of k (A000005). - _Wesley Ivan Hurt_, Nov 16 2017
%F A212151 G.f.: (x/(1-x))*(Sum_{i>=1} x^i/(1-x^i))^2. - _Robert Israel_, Nov 16 2017
%F A212151 from _Ridouane Oudra_, Oct 10 2023: (Start)
%F A212151 a(n) = Sum_{i=1..n-1} Sum_{j=1..n-1} tau(i*j)*floor((n-1)/(i+j)) ;
%F A212151 a(n) = Sum_{i=1..n-1} Sum_{j=1..i-1} tau(j)*tau(i-j) ;
%F A212151 a(n+2) = Sum_{i=1..n} A055507(i). (End)
%p A212151 N:= 100: # to get a(0)..a(N)
%p A212151 g:= z*(1-z)^(-1)*add(z^i/(1-z^i),i=1..N-2)^2:
%p A212151 S:=series(g,z,N+1):
%p A212151 seq(coeff(S,z,n),n=0..N); # _Robert Israel_, Nov 16 2017
%t A212151 t = Compile[{{n, _Integer}}, Module[{s = 0},
%t A212151 (Do[If[w*x + y*z < n, s = s + 1],
%t A212151 {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
%t A212151 Map[t[#] &, Range[0, 40]]  (* A212151 *)
%t A212151 (* _Peter J. C. Moses_, Apr 13 2012 *)
%o A212151 (Python)
%o A212151 from sympy import divisor_count
%o A212151 def A212151(n): return  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 A212151 Cf. A000005, A211795, A212240.
%Y A212151 Cf. A055507.
%K A212151 nonn,easy
%O A212151 0,5
%A A212151 _Clark Kimberling_, May 07 2012