A321490 - OEIS

%I #11 Nov 24 2018 01:06:45

%S 4,15,32,40,65,108,85,120,175,256,156,203,272,369,500,259,320,405,520,

%T 671,864,400,477,580,715,888,1105,1372,585,680,803,960,1157,1400,1695,

%U 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

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

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

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

%e The table starts:

%e Row 1:    4;

%e Row 2:   15,  32;

%e Row 3:   40,  65, 108;

%e Row 4:   85, 120, 175, 256;

%e Row 5:  156, 203, 272, 369,  500;

%e Row 6:  259, 320, 405, 520,  671,  864;

%e Row 7:  400, 477, 580, 715,  888, 1105, 1372;

%e Row 8:  585, 680, 803, 960, 1157, 1400, 1695, 2048;

%e etc.

%t 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 *)

%o (PARI) A321490(n,k)=(n+k)*(n^2+k^2)

%o A321490_row(n)=vector(n,k,(n+k)*(n^2+k^2))

%o A321490_list(N=12)=concat(apply(A321490_row,[1..N]))

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

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

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

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

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

%K nonn,tabl,easy

%O 1,1

%A _M. F. Hasler_, Nov 22 2018