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A253015 Sequence of determinants of matrices based on the digits of nonnegative integers. 1
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -1, 1, -1, -5, -11, -19, -29, -41, -55, -71, -4, -1, 4, 1, -4, -11, -20, -31, -44, -59, -9, -5, 1, 9, 5, -1, -9, -19, -31, -45, -16, -11, -4, 5, 16, 11, 4, -5, -16 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A given nonnegative integer is transformed into a square matrix whose order equals the quantity of the number's digits. Each element of the main diagonal is a digit of this original number, while other elements are calculated from this diagonal. The determinant of this matrix is the element of the sequence.

LINKS

Filipi R. de Oliveira, Table of n, a(n) for n = 0..999

FORMULA

a(n) = det(B) where B is the n X n matrix with B(i,i) given by the i-th digit of n, B(i,j) = abs(B(i,j-1)-B(i+1,j)) if i < j and B(i,j) = B(i-1,j) + B(i,j+1) if i > j.

EXAMPLE

For n=124, a(124)=2, as follows:

B(1,1) = 1;

B(2,2) = 2;

B(3,3) = 4;

B(1,2) = abs(B(1,1) - B(2,2)) = abs(1-2) = 1;

B(2,3) = abs(B(2,2) - B(3,3)) = abs(2-4) = 2;

B(1,3) = abs(B(1,2) - B(2,3)) = abs(1-1) = 1;

B(2,1) = B(1,1) + B(2,2) = 1 + 2 = 3;

B(3,2) = B(2,2) + B(3,3) = 2 + 4 = 6;

B(3,1) = B(2,1) + B(3,2) = 3 + 6 = 9.

Thus,

_______|1 1 1|

B(124)=|3 2 2| --> det(B(124)) = a(124) = 2.

_______|9 6 4|

CROSSREFS

See A227876, since the process of matrix construction is this so-called "pyramidalization".

Sequence in context: A216587 A174210 A134777 * A257295 A004427 A113230

Adjacent sequences:  A253012 A253013 A253014 * A253016 A253017 A253018

KEYWORD

sign,base,easy,dumb

AUTHOR

Filipi R. de Oliveira, Dec 25 2014

STATUS

approved

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Last modified September 22 05:11 EDT 2021. Contains 347605 sequences. (Running on oeis4.)