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A212151
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Number of 2 X 2 matrices M of positive integers such that permanent(M) < n.
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4
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0, 0, 0, 1, 5, 13, 27, 47, 75, 112, 156, 214, 278, 358, 444, 552, 660, 796, 930, 1099, 1259, 1457, 1649, 1885, 2101, 2377, 2623, 2933, 3221, 3569, 3879, 4279, 4623, 5056, 5452, 5926, 6334, 6878, 7328, 7892, 8404, 9018, 9540, 10228, 10788, 11504, 12142, 12898
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OFFSET
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0,5
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COMMENTS
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For a guide to related sequences, see A211795.
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LINKS
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FORMULA
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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
G.f.: (x/(1-x))*(Sum_{i>=1} x^i/(1-x^i))^2. - Robert Israel, Nov 16 2017
a(n) = Sum_{i=1..n-1} Sum_{j=1..n-1} tau(i*j)*floor((n-1)/(i+j)) ;
a(n) = Sum_{i=1..n-1} Sum_{j=1..i-1} tau(j)*tau(i-j) ;
a(n+2) = Sum_{i=1..n} A055507(i). (End)
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MAPLE
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N:= 100: # to get a(0)..a(N)
g:= z*(1-z)^(-1)*add(z^i/(1-z^i), i=1..N-2)^2:
S:=series(g, z, N+1):
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MATHEMATICA
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t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w*x + y*z < n, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212151 *)
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PROG
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(Python)
from sympy import divisor_count
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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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