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A095873
Triangle T(n,k) = (2*k-1)*(n+k-1)*(n-k+1) read by rows, 1<=k<=n.
1
1, 4, 9, 9, 24, 25, 16, 45, 60, 49, 25, 72, 105, 112, 81, 36, 105, 160, 189, 180, 121, 49, 144, 225, 280, 297, 264, 169, 64, 189, 300, 385, 432, 429, 364, 225, 81, 240, 385, 504, 585, 616, 585, 480, 289, 100, 297, 480, 637, 756, 825
OFFSET
1,2
COMMENTS
Matrix square of A158405.
REFERENCES
Albert H. Beiler, "Recreations in the Theory of Numbers", Dover, 1966.
FORMULA
T(n,k) = (2*k-1)*A094728(n,k).
Sum_{k=1..n} T(n,k)= n*(n+1)*(3*n^2+n-1)/6 = A103220(n). - R. J. Mathar, Oct 30 2011
EXAMPLE
[1 0 0 / 1 3 0 / 1 3 5]^2 = [1 0 0 / 4 9 0 / 9 24 25]. Delete the zeros and
read by rows:
1;
4, 9;
9, 24, 25;
16,45, 60, 49;
25,72,105,112, 81;
MAPLE
A095873 := proc(n, k)
(2*k-1)*(n+k-1)*(n-k+1) ;
end proc:
seq(seq(A095873(n, k), k=1..n), n=1..13) ; # R. J. Mathar, Oct 30 2011
MATHEMATICA
Table[(2k-1)(n+k-1)(n-k+1), {n, 10}, {k, n}]//Flatten (* Harvey P. Dale, May 03 2018 *)
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Gary W. Adamson, Jun 10 2004
EXTENSIONS
Definition in closed form by R. J. Mathar, Oct 30 2011
STATUS
approved