OFFSET

1,2

COMMENTS

LINKS

FORMULA

When m and n define a row of triples in A338275 that gives rise to a triple (a row) of A338895, the current term corresponding to such a row is (m-n-1)*n/2.

If [a,b,c] is the n-th row of A338895, then a(n) = a*b/(a+b+c).

T(n, k) = 2*k*(n - k). Follows from the first comment. - Peter Luschny, Apr 17 2023

EXAMPLE

m 3

n 2 [0,4,4] 0

------------------

m 5

n 2 [6,8,10] 2

n 4 [0,16,16] 0

------------------

m 7

n 2 [16,12,20] 4

n 4 [10,24,26] 4

n 6 [0,36,36] 0

------------------

m 9

n 2 [30,16,34] 6

n 4 [24,32,40] 8

n 6 [14,48,50] 6

n 8 [0,64,64] 0

------------------.

The 7th row of A338895 is [30,16,34], so a(7) = 30*16/(30+16+34) = 6.

As a triangle:

0

2, 0

4, 4, 0

6, 8, 6, 0

8, 12, 12, 8, 0

10, 16, 18, 16, 10, 0

12, 20, 24, 24, 20, 12, 0,

MATHEMATICA

Table[#1 #2/Total[{##}] & @@ {((#1 - 1)^2 - #2^2)/2, (#1 - 1) #2, ((#1 - 1)^2 + #2^2)/2} & @@ {m, n}, {m, 3, 23, 2}, {n, 2, m, 2}] // Flatten (* Michael De Vlieger, Dec 04 2020 *)

PROG

(PARI) lista(mm) = forstep (m=3, mm, 2, forstep (n=2, m, 2, my(v=[((m-1)^2 - n^2)/2, (m-1)*n, ((m-1)^2 + n^2)/2]); print1(v[1]*v[2]/vecsum(v), ", "))); \\ Michel Marcus, Dec 04 2020

CROSSREFS

KEYWORD

nonn,tabl

AUTHOR

David Lovler, Nov 14 2020

STATUS

approved