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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
KEYWORD
sign,base,easy,dumb
AUTHOR
STATUS
approved

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Last modified July 15 14:56 EDT 2024. Contains 374333 sequences. (Running on oeis4.)