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A121682 Triangle read by rows: T(i,j) = (T(i-1,j) + i)*i. 2
1, 6, 4, 27, 21, 9, 124, 100, 52, 16, 645, 525, 285, 105, 25, 3906, 3186, 1746, 666, 186, 36, 27391, 22351, 12271, 4711, 1351, 301, 49, 219192, 178872, 98232, 37752, 10872, 2472, 456, 64, 1972809, 1609929, 884169, 339849, 97929, 22329, 4185, 657, 81, 19728190, 16099390, 8841790, 3398590, 979390, 223390, 41950, 6670, 910, 100 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The first column is A030297 = a(n) = n*(n+a(n-1)). The main diagonal are the squares A000290 = n^2. The first lower diagonal (6,21,52,...) is A069778 = q-factorial numbers 3!_q. See also A121662.
REFERENCES
T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.
LINKS
EXAMPLE
Triangle begins:
1
6 4
27 21 9
124 100 52 16
645 525 285 105 25
3906 3186 1746 666 186 36
27391 22351 12271 4711 1351 301 49
...
MAPLE
T:= proc(i, j) option remember;
`if`(j<1 or j>i, 0, (T(i-1, j)+i)*i)
end:
seq(seq(T(n, k), k=1..n), n=1..10); # Alois P. Heinz, Jun 22 2022
MATHEMATICA
T[n_, k_] /; 1 <= k <= n := T[n, k] = (T[n-1, k]+n)*n;
T[_, _] = 0;
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 17 2022 *)
PROG
(Python)
def T(i, j): return (T(i-1, j)+i)*i if 1 <= j <= i else 0
print([T(r, c) for r in range(1, 11) for c in range(1, r+1)]) # Michael S. Branicky, Jun 22 2022
CROSSREFS
Row sums give A337001.
Sequence in context: A129886 A133837 A211945 * A237425 A191567 A274707
KEYWORD
nonn,tabl
AUTHOR
Thomas Wieder, Aug 15 2006
EXTENSIONS
Edited by N. J. A. Sloane, Sep 15 2006
Formula in name corrected by Alois P. Heinz, Jun 22 2022
STATUS
approved

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Last modified May 23 05:11 EDT 2024. Contains 372758 sequences. (Running on oeis4.)