A080692 - OEIS

%I #21 Aug 23 2024 10:20:13

%S 0,1,3,8,18,40,88,192,400,832,1728,3584,7424,15360,31744,65536,133120,

%T 270336,548864,1114112,2260992,4587520,9306112,18874368,38273024,

%U 77594624,157286400,318767104,645922816,1308622848,2650800128

%N a(n)=(-1)^(n+1)*det(M(n)) where M(n) is the n X n matrix M(i,j)=min(abs(i-j),i).

%C A001787(n-1) is the determinant of the n X n matrix M(i,j)=min(abs(i-j),i+j)

%H Vaclav Kotesovec, <a href="/A080692/b080692.txt">Table of n, a(n) for n = 1..1000</a>

%H Vaclav Kotesovec, <a href="/A080692/a080692.jpg">Graph - the asymptotic ratio (10000 terms)</a>

%F a(n) = 2*a(n-1) + 2^floor(n-log(n)/log(2)-1) = 2*a(n-1) + A054243(n). [corrected by _Vaclav Kotesovec_, Aug 23 2024]

%F a(n) ~ 2^(n-1) * (c*(log(n) + gamma) - 1), where gamma is the Euler-Mascheroni constant A001620 and 1/2 < c < 1. Conjecture: c = 1/sqrt(2). - _Vaclav Kotesovec_, Aug 23 2024

%e M(5) is [0 1 1 1 1] [1 0 1 2 2] [2 1 0 1 2] [3 2 1 0 1] [4 3 2 1 0].

%t Table[(-1)^(n+1) * Det[Table[Min[Abs[i-j], i], {i, 1, n}, {j, 1, n}]], {n, 1, 30}] (* _Vaclav Kotesovec_, Aug 23 2024 *)

%o (PARI) a(n)=(-1)^(n+1)*matdet(matrix(n,n,i,j,min(abs(i-j),i)))

%Y Cf. A054243, A001787.

%K nonn

%O 1,3

%A _Benoit Cloitre_, Mar 03 2003