A307651 a(n) is the determinant of the Vandermonde matrix of the digits of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, -7, -6, -5, -4, -3, -2, -1, 0

Offset: 0

Author

Rémy Sigrist, Apr 20 2019

Keywords

• sign
• base

Examples

			             | 2^0 2^1 2^2 |
a(234) = det | 3^0 3^1 3^2 | = 2.
             | 4^0 4^1 4^2 |
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Wikipedia, Vandermonde matrix

Crossrefs

See A307710 for the factorial base variant.

Cf. A007376, A010784, A177894, A307586, A307587.

Programs

PARI

a(n) = my (d=digits(n)); matdet(matrix(#d,#d,r,c,d[r]^(c-1)))

Formula

a(n) != 0 iff n belongs to A010784.

a(n) = 0 for any n > 9876543210.