

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



FORMULA

a(n) = det(B) where B is the n X n matrix with B(i,i) given by the ith digit of n, B(i,j) = abs(B(i,j1)B(i+1,j)) if i < j and B(i,j) = B(i1,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(12) = 1;
B(2,3) = abs(B(2,2)  B(3,3)) = abs(24) = 2;
B(1,3) = abs(B(1,2)  B(2,3)) = abs(11) = 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 socalled "pyramidalization".


KEYWORD

sign,base,easy,dumb


AUTHOR



STATUS

approved



