A080692 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).

0, 1, 3, 8, 18, 40, 88, 192, 400, 832, 1728, 3584, 7424, 15360, 31744, 65536, 133120, 270336, 548864, 1114112, 2260992, 4587520, 9306112, 18874368, 38273024, 77594624, 157286400, 318767104, 645922816, 1308622848, 2650800128

Offset: 1

Author

Benoit Cloitre, Mar 03 2003

Keywords

• nonn

Comments

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

Examples

			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].
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..1000
• Vaclav Kotesovec, Graph - the asymptotic ratio (10000 terms)

Crossrefs

Cf. A054243, A001787.

Programs

Mathematica

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 *)

PARI

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

Formula

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]

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