A256560 Triangle read by rows, sums of 2 distinct nonzero squares plus sums of 2 distinct nonzero cubes: T(n,k) = n^2 + k^2 + n^3 + k^3, 1 <= k <= n-1.

14, 38, 48, 82, 92, 116, 152, 162, 186, 230, 254, 264, 288, 332, 402, 394, 404, 428, 472, 542, 644, 578, 588, 612, 656, 726, 828, 968, 812, 822, 846, 890, 960, 1062, 1202, 1386, 1102, 1112, 1136, 1180, 1250, 1352, 1492, 1676, 1910

Offset

2,1

Comments

All terms are even.

T(n,1) = A011379(n) + 2.

When n=k+1, T(n,k+1) = A011379(n-1) + A011379(n) = 2n^3 - n^2 + n.

Links

Table of n, a(n) for n=2..46.

Formula

a(n) = A055096(n) + A256497(n-1).

T(n,k) = T055096(n,k) + T256547(n-1,k).

T(n,k) = T(n-1,k) + A049450(n).

T(n,k) = T(n,k-1) + A049450(k).

T(n,k) = A011379(n) + A011379(k).

Example

Triangle starts T(2,1):
n\k   1    2    3    4    5    6    7     8    9   10
2:   14
3:   38   48
4:   82   92   116
5:   152  162  186  230
6:   254  264  288  332  402
7:   394  404  428  472  542  644
8:   578  588  612  656  726  828  968
9:   812  822  846  890  960  1062 1202 1386
10:  1102 1112 1136 1180 1250 1352 1492 1676 1910
11:  1454 1464 1488 1532 1602 1704 1844 2028 2262 2552
...
The successive terms are: (2^2 + 1^2 + 2^3 + 1^3), (3^2 + 1^2 + 3^3 + 1^3), (3^2 + 2^2 + 3^3 + 2^3), (4^2 + 1^2 + 4^3 + 1^3), (4^2 + 2^2 + 4^3 + 2^3), (4^2 + 3^2 + 4^3 + 3^3), ...
T(7,4) = 472 because 7^2 + 7^3 + 4^2 + 4^3 = 472.

Crossrefs

Cf. A055096 (sums of 2 distinct nonzero squares), A256497 (sums of 2 distinct nonzero cubes), A011379, A024670, A004431, A049450.

Sequence in context: A034181 A216766 A057439 * A058826 A142241 A186121

Adjacent sequences: A256557 A256558 A256559 * A256561 A256562 A256563

Keyword

nonn,tabl

Author

Bob Selcoe, Apr 02 2015

Status

approved