A373102 - OEIS

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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

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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.