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A141429
Triangle T(n, k) = (k+1)*(n-k+1), read by rows.
1
2, 4, 3, 6, 6, 4, 8, 9, 8, 5, 10, 12, 12, 10, 6, 12, 15, 16, 15, 12, 7, 14, 18, 20, 20, 18, 14, 8, 16, 21, 24, 25, 24, 21, 16, 9, 18, 24, 28, 30, 30, 28, 24, 18, 10, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12, 24, 33, 40, 45, 48, 49, 48, 45, 40, 33, 24, 13
OFFSET
1,1
FORMULA
T(n, k) = (k+1)*(n-k+1).
T(n, k) = A158823(n+2, k+2).
Sum_{k=1..n} T(n, k) = A005581(n+1).
EXAMPLE
Triangle begins as:
2;
4, 3;
6, 6, 4;
8, 9, 8, 5;
10, 12, 12, 10, 6;
12, 15, 16, 15, 12, 7;
14, 18, 20, 20, 18, 14, 8;
16, 21, 24, 25, 24, 21, 16, 9;
18, 24, 28, 30, 30, 28, 24, 18, 10;
20, 27, 32, 35, 36, 35, 32, 27, 20, 11;
MAPLE
A141429 := proc(n, k)
(k+1)*(n-k+1) ;
end proc:
seq(seq(A141429(n, m), m=1..n), n=1..14) ; # R. J. Mathar, Nov 10 2011
MATHEMATICA
Table[(k+1)*(n-k+1), {n, 15}, {k, n}]//Flatten
PROG
(Magma) [(k+1)*(n-k+1): k in [1..n], n in [1..15]]; // G. C. Greubel, Mar 30 2021
(Sage) flatten([[(k+1)*(n-k+1) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Mar 30 2021
CROSSREFS
KEYWORD
nonn,easy,tabl
AUTHOR
EXTENSIONS
Edited by G. C. Greubel, Mar 30 2021
STATUS
approved