cp's OEIS Frontend

A211149 Number of 2 X 2 nonsingular matrices having all terms in {-n,...,0,...,n}.

%I A211149 #6 Jan 14 2017 09:41:11
%S A211149 48,496,2112,6016,13808,27248,48896,81152,127280,190576,275264,384768,
%T A211149 524784,699376,914176,1175040,1488688,1860208,2298304,2808320,3399280,
%U A211149 4079088,4856704,5738624,6736944,7859824,9117376,10519424
%N A211149 Number of 2 X 2 nonsingular matrices having all terms in {-n,...,0,...,n}.
%C A211149 A211149(n) + A209981(n) = (2n+1)^4 for n>0.
%C A211149 It appears that 16 divides A211149(n).
%C A211149 For a guide to related sequences, see A210000.
%t A211149 a = -n; b = n; z1 = 30;
%t A211149 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A211149 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211149 Table[c[n, 0], {n, 1, z1}]   (* A209981 *)
%t A211149 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 1, m}]
%t A211149 t = Table[c1[n, 2*n^2], {n, 1, z1}]   (* A211148 *)
%t A211149 2 t   (* A211149 *)
%t A211149 t/8   (* integers *)
%Y A211149 Cf. A210000.
%K A211149 nonn
%O A211149 1,1
%A A211149 _Clark Kimberling_, Apr 04 2012