A174647 Determinant of the matrix a(i,j) = 1 if abs(i-j) < 2 and -1 in the rest.

-4, 0, 0, 0, -64, 0, 256, 1024, 0, -4096, -12288, 0, 49152, 131072, 0, -524288, -1310720, 0, 5242880, 12582912, 0, -50331648, -117440512, 0, 469762048, 1073741824, 0, -4294967296, -9663676416, 0, 38654705664, 85899345920, 0

Offset

3,1

Links

Table of n, a(n) for n=3..35.

Formula

Empirical g.f.: -4*x^3*(8*x^3+4*x^2-2*x+1) / ((2*x+1)*(4*x^2-2*x+1)^2). - Colin Barker, Jun 20 2013

Example

a(7) = Det({ {1, 1, -1, -1, -1, -1, -1}, {1, 1, 1, -1, -1, -1, -1}, {-1, 1, 1, 1, -1, -1, -1}, {-1, -1, 1, 1, 1, -1, -1}, {-1, -1, -1, 1, 1, 1, -1}, {-1, -1, -1, -1, 1, 1, 1}, {-1, -1, -1, -1, -1, 1, 1} }) = -64.

Prog

(PARI) a(n) = matdet(matrix(n, n, i, j, if(abs(i-j)<2, 1, -1))) \\ Jason Yuen, Feb 08 2025

Crossrefs

Sequence in context: A057386 A099306 A228630 * A258644 A169770 A287633

Adjacent sequences: A174644 A174645 A174646 * A174648 A174649 A174650

Keyword

sign,changed

Author

José María Grau Ribas, Mar 25 2010

Status

approved