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A360373
Triangular array T read by rows related to the multiplication table.
0
1, 2, 4, 2, 3, 6, 9, 6, 3, 4, 8, 12, 16, 12, 8, 4, 5, 10, 15, 20, 25, 20, 15, 10, 5, 6, 12, 18, 24, 30, 36, 30, 24, 18, 12, 6, 7, 14, 21, 28, 35, 42, 49, 42, 35, 28, 21, 14, 7, 8, 16, 24, 32, 40, 48, 56, 64, 56, 48, 40, 32, 24, 16, 8, 9, 18, 27, 36, 45, 54, 63, 72, 81
OFFSET
1,2
FORMULA
T(n, k) = T(n, 2*n-k) = n*k for 1<=k<=n .
Sum_{k=1..2*n-1} T(n, k) = n^3.
Sum_{k=1..2*n-1} T(n, k)^2 = n^3*(2*n^2 + 1)/3 = A272125(n).
T(n, k) = n * A004737(n,k).
EXAMPLE
Table T(n, k) , n>=1 , 1<=k<=2*n-1.
n = 1 : 1 ;
n = 2 : 2, 4, 2 ;
n = 3 : 3, 6, 9, 6, 3 ;
n = 4 : 4, 8, 12, 16, 12, 8, 4 ;
n = 5 : 5, 10, 15, 20, 25, 20, 15, 10, 5 ;
n = 6 : 6, 12, 18, 24, 30, 36, 30, 24, 18, 12, 6 ;
n = 7 : 7, 14, 21, 28, 35, 42, 49, 42, 35, 28, 21, 14, 7 ;
n = 8 : 8, 16, 24, 32, 40, 48, 56, 64, 56, 48, 40, 32, 24, 16, 8 ;
...
MAPLE
T:= (n, k)-> n*min(k, 2*n-k):
seq(seq(T(n, k), k=1..2*n-1), n=1..10); # Alois P. Heinz, Feb 04 2023
CROSSREFS
Cf. A000290 (central terms), A000578 (row sums), A060747 (row lengths).
Sequence in context: A348486 A331279 A151849 * A141387 A349400 A335678
KEYWORD
nonn,tabf
AUTHOR
Philippe Deléham, Feb 04 2023
STATUS
approved