cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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.

Original entry on oeis.org

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

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Author

Bob Selcoe, Apr 02 2015

Keywords

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.

Examples

			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.

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).
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