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
KEYWORD
sign,base,easy,dumb
AUTHOR
Filipi R. de Oliveira, Dec 25 2014
STATUS
approved