A321490 Triangular table T[n,k] = (n+k)(n^2+k^2), 1 <= k <= n = 1, 2, 3, ...; read by rows.

4, 15, 32, 40, 65, 108, 85, 120, 175, 256, 156, 203, 272, 369, 500, 259, 320, 405, 520, 671, 864, 400, 477, 580, 715, 888, 1105, 1372, 585, 680, 803, 960, 1157, 1400, 1695, 2048, 820, 935, 1080, 1261, 1484, 1755, 2080, 2465, 2916, 1111, 1248, 1417, 1624, 1875, 2176, 2533, 2952, 3439, 4000, 1464, 1625, 1820, 2055, 2336

Offset: 1

Author

M. F. Hasler, Nov 22 2018

Keywords

• nonn
• tabl
• easy

Examples

			The table starts:
Row 1:    4;
Row 2:   15,  32;
Row 3:   40,  65, 108;
Row 4:   85, 120, 175, 256;
Row 5:  156, 203, 272, 369,  500;
Row 6:  259, 320, 405, 520,  671,  864;
Row 7:  400, 477, 580, 715,  888, 1105, 1372;
Row 8:  585, 680, 803, 960, 1157, 1400, 1695, 2048;
etc.
		

Crossrefs

Cf. A321491 (numbers of the form T(n,k) with n > k > 0).

Cf. A321492 (numbers which can be written at least twice in this form).

Cf. A033430 (diagonal), A053698 (column 1).

Cf. A198063 (read as a square array equals T(n,k) for all n, k >= 0).

Cf. A321500 (variant of this table with additional row 0 and column 0).

Programs

Mathematica

t[n_, k_] := (n + k) (n^2 + k^2); Table[t[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Amiram Eldar, Nov 22 2018 *)

PARI

A321490(n,k)=(n+k)*(n^2+k^2)
A321490_row(n)=vector(n,k,(n+k)*(n^2+k^2))
A321490_list(N=12)=concat(apply(A321490_row,[1..N]))

Formula

Diagonal: T(n,n) = 4*n^3 = A033430(n).

Column 1: T(n,1) = (n + 1)(n^2 + 1) = A053698(n) = (n^4-1)/(n-1) for n > 1.