cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Philippe Deléham, Feb 04 2023

Keywords

Examples

			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 ;
...
		

Crossrefs

Cf. A000290 (central terms), A000578 (row sums), A060747 (row lengths).

Programs

  • 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

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).
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