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A307651 a(n) is the determinant of the Vandermonde matrix of the digits of n. 2

%I #15 Apr 26 2019 02:31:31

%S 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,

%T -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,

%U -5,-4,-3,-2,-1,0,1,2,3,-7,-6,-5,-4,-3,-2,-1,0

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

%H Rémy Sigrist, <a href="/A307651/b307651.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Vandermonde_matrix">Vandermonde matrix</a>

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

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

%e | 2^0 2^1 2^2 |

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

%e | 4^0 4^1 4^2 |

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

%Y See A307710 for the factorial base variant.

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

%K sign,base

%O 0,14

%A _Rémy Sigrist_, Apr 20 2019

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Last modified March 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)