A280391 Number of 2 X 2 matrices with all elements in {0,...,n} with permanent = determinant * n.
1, 12, 25, 57, 81, 141, 169, 259, 297, 413, 441, 621, 625, 825, 873, 1079, 1089, 1403, 1369, 1739, 1729, 2021, 2025, 2507, 2433, 2859, 2905, 3301, 3249, 4029, 3721, 4509, 4305, 4793, 4989, 5551, 5329, 6027, 6025, 6807, 6561, 7917, 7225, 8357, 8121, 8677, 8649, 9843, 9481, 10889
Offset: 0
Keywords
Links
- Robert Israel and Indranil Ghosh, Table of n, a(n) for n = 0..1600 (n = 0..200 from Indranil Ghosh)
Crossrefs
Cf. A280321 (Number of 2 X 2 matrices with all elements in {0,..,n} with permanent*n = determinant).
Cf. A015237 (Number of 2 X 2 matrices having all elements in {0..n} with determinant = permanent).
Cf. A016754 (Number of 2 X 2 matrices having all elements in {0..n} with determinant =2* permanent).
Cf. A280364 (Number of 2 X 2 matrices having all elements in {0..n} with determinant^n = permanent).
Programs
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Maple
g:= proc(r,n) if r = 0 then 2*n+1 else nops(select(t -> t <= n and r <= t*n, numtheory:-divisors(r))) fi end proc: f:= proc(n) local c; if n::even then (2*n+1)^2 + add(g((n+1)*c,n)*g((n-1)*c,n), c=1..n-1) else (2*n+1)^2 + add(g((n+1)/2*c,n) * g((n-1)/2*c,n), c=1..2*n-1) fi end proc: map(f, [$0..100]); # Robert Israel, Jan 02 2017 -
Mathematica
g[r_, n_] := If[r == 0, 2n + 1, Length[Select[Divisors[r], # <= n && r <= # n&]]]; f[n_] := If[EvenQ[n], (2n + 1)^2 + Sum[g[(n + 1)c, n] g[(n - 1)c, n], {c, 1, n - 1}], (2n + 1)^2 + Sum[g[(n + 1)/2 c, n] g[(n - 1)/2 c, n], {c, 1, 2n - 1}]]; f /@ Range[0, 100] (* Jean-François Alcover, Jul 29 2020, after Robert Israel *) -
Python
def t(n): s=0 for a in range(0,n+1): for b in range(0,n+1): for c in range(0,n+1): for d in range(0,n+1): if (a*d-b*c)*n==(a*d+b*c): s+=1 return s for i in range(0,201): print(t(i))
Comments