A104583 - OEIS

%I #11 Feb 07 2022 00:07:09

%S 1,4,2,9,8,1,16,18,4,2,25,32,9,8,1,36,50,16,18,4,2,49,72,25,32,9,8,1,

%T 64,98,36,50,16,18,4,2,81,128,49,72,25,32,9,8,1,100,162,64,98,36,50,

%U 16,18,4,2,121,200,81,128,49,72,25,32,9,8,1,144,242,100,162,64,98,36,50,16,18

%N Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product A*B of the matrices A = [1; 3,1; 5,3,1; 7,5,3,1; ...]; B = [1; 1,2; 1,2,1; 1,2,1,2; ...] (both infinite lower triangular matrices).

%F T(i, j) = (i-j+1)^2 if j <= i and j is odd; 2(i-j+1)^2 if j <= i and j is even; 0 if j > i. - _Emeric Deutsch_, Mar 23 2005

%e The first few rows are:

%e    1;

%e    4,  2;

%e    9,  8,  1;

%e   16, 18,  4,  2;

%e   25, 32,  9,  8,  1;

%e   36, 50, 16, 18,  4,  2;

%e   49, 72, 25, 32,  9,  8,  1;

%e   ...

%p T:=proc(i,j) if j<=i and j mod 2=1 then (i-j+1)^2 elif j<=i and j mod 2 =0 then 2*(i-j+1)^2 else 0 fi end: for i from 1 to 13 do seq(T(i,j),j=1..i) od; # yields sequence in triangular form # _Emeric Deutsch_, Mar 23 2005

%Y Cf. A002411.

%Y Row sums yield the pentagonal pyramidal numbers (A002411).

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Mar 16 2005

%E More terms from _Emeric Deutsch_, Mar 23 2005