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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.

%I A256560 #23 Apr 03 2015 13:10:38
%S A256560 14,38,48,82,92,116,152,162,186,230,254,264,288,332,402,394,404,428,
%T A256560 472,542,644,578,588,612,656,726,828,968,812,822,846,890,960,1062,
%U A256560 1202,1386,1102,1112,1136,1180,1250,1352,1492,1676,1910
%N 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.
%C A256560 All terms are even.
%C A256560 T(n,1) = A011379(n) + 2.
%C A256560 When n=k+1, T(n,k+1) = A011379(n-1) + A011379(n) = 2n^3 - n^2 + n.
%F A256560 a(n) = A055096(n) + A256497(n-1).
%F A256560 T(n,k) = T055096(n,k) + T256547(n-1,k).
%F A256560 T(n,k) = T(n-1,k) + A049450(n).
%F A256560 T(n,k) = T(n,k-1) + A049450(k).
%F A256560 T(n,k) = A011379(n) + A011379(k).
%e A256560 Triangle starts T(2,1):
%e A256560 n\k   1    2    3    4    5    6    7     8    9   10
%e A256560 2:   14
%e A256560 3:   38   48
%e A256560 4:   82   92   116
%e A256560 5:   152  162  186  230
%e A256560 6:   254  264  288  332  402
%e A256560 7:   394  404  428  472  542  644
%e A256560 8:   578  588  612  656  726  828  968
%e A256560 9:   812  822  846  890  960  1062 1202 1386
%e A256560 10:  1102 1112 1136 1180 1250 1352 1492 1676 1910
%e A256560 11:  1454 1464 1488 1532 1602 1704 1844 2028 2262 2552
%e A256560 ...
%e A256560 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), ...
%e A256560 T(7,4) = 472 because 7^2 + 7^3 + 4^2 + 4^3 = 472.
%Y A256560 Cf. A055096 (sums of 2 distinct nonzero squares), A256497 (sums of 2 distinct nonzero cubes), A011379, A024670, A004431, A049450.
%K A256560 nonn,tabl
%O A256560 2,1
%A A256560 _Bob Selcoe_, Apr 02 2015