A121682 Triangle read by rows: T(i,j) = (T(i-1,j) + i)*i.

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

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

Table of n, a(n) for n=1..55.

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

Cf. A030297, A000290, A069778, A121662.

Row sums give A337001.

Sequence in context: A129886 A133837 A211945 * A237425 A191567 A274707

Adjacent sequences: A121679 A121680 A121681 * A121683 A121684 A121685

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