A360373 Triangular array T read by rows related to the multiplication table.

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

Links

Table of n, a(n) for n=1..73.

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).

Cf. A003991, A004737, A075362, A272125 .

Sequence in context: A348486 A331279 A151849 * A141387 A349400 A335678

Adjacent sequences: A360370 A360371 A360372 * A360374 A360375 A360376

Keyword

nonn,tabf

Author

Philippe Deléham, Feb 04 2023

Status

approved