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

1,1

Links

Table of n, a(n) for n=1..60.

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.

Example

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.

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 *)

Prog

(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]))

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).

Sequence in context: A366659 A121914 A336607 * A270710 A322571 A110341

Adjacent sequences: A321487 A321488 A321489 * A321491 A321492 A321493

Keyword

nonn,tabl,easy

Author

M. F. Hasler, Nov 22 2018

Status

approved