A373102 Determinants of Hankel matrices corresponding to digits of numbers with an odd number of digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -36, -35, -34, -33, -32, -31, -30

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a((21 + 100^(i + 1))/11 + 100*x + z + 1) = a((21 + 100^(i + 1))/11 + 100*x + z) + a((21 + 100^i)/11 + x) for 0 <= x < 9 * 10^i, 0 <= z <= 98 with z !== 9 (mod 10).

Example

a(13) = 2 because the 13th number with an odd number of digits is 102 and the Hankel matrix
[ 1 0 ]
[ 0 2 ]
formed from the digits 1,0,2 has determinant 2.

Maple

f:= proc(n)
    Determinant(HankelMatrix(convert(n, base, 10)))
end proc;
map(f, [$0..9, $100..999]);

Crossrefs

Cf. A373066.

Sequence in context: A187844 A007954 A079475 * A081286 A080867 A095187

Adjacent sequences: A373095 A373096 A373101 * A373103 A373104 A373105

Keyword

sign,base,look

Author

Robert Israel, May 23 2024

Status

approved