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A238339 Square number array read by ascending antidiagonals: T(1,k) = 2*k + 1, and T(n,k) = (2*n^(k+1)-n-1)/(n-1) otherwise.

%I A238339 #11 Oct 14 2023 14:04:39
%S A238339 1,1,1,1,3,1,1,5,5,1,1,7,13,7,1,1,9,25,29,9,1,1,11,41,79,61,11,1,1,13,
%T A238339 61,169,241,125,13,1,1,15,85,311,681,727,253,15,1,1,17,113,517,1561,
%U A238339 2729,2185,509,17,1,1,19,145,799,3109,7811,10921,6559,1021,19,1
%N A238339 Square number array read by ascending antidiagonals: T(1,k) = 2*k + 1, and T(n,k) = (2*n^(k+1)-n-1)/(n-1) otherwise.
%F A238339 T(0,k) = A000012(k) = 1;
%F A238339 T(1,k) = A005408(k) = 2k+1;
%F A238339 T(2,k) = A036563(k+2);
%F A238339 T(3,k) = A058481(k+1);
%F A238339 T(4,k) = A083584(k);
%F A238339 T(5,k) = A137410(k);
%F A238339 T(6,k) = A233325(k);
%F A238339 T(7,k) = A233326(k);
%F A238339 T(8,k) = A233328(k);
%F A238339 T(9,k) = A211866(k+1);
%F A238339 T(10,k) = A165402(k+1);
%F A238339 T(n,0) = A000012(n) = 1;
%F A238339 T(n,1) = A005408(n) = 2*n+1;
%F A238339 T(n,2) = A001844(n) = 2*n^2 + 2*n + 1.
%e A238339 Square array begins:
%e A238339 1..1...1.....1......1.......1........1........1...
%e A238339 1..3...5.....7......9......11.......13.......15...
%e A238339 1..5..13....29.....61.....125......253......509...
%e A238339 1..7..25....79....241.....727.....2185.....6559...
%e A238339 1..9..41...169....681....2729....10921....43689...
%e A238339 1.11..61...311...1561....7811....39061...195311...
%e A238339 1.13..85...517...3109...18661...111973...671845...
%e A238339 1.15.113...799...5601...39215...274513..1921599...
%e A238339 1.17.145..1169...9361...74897...599185..4793489...
%e A238339 1.19.181..1639..14761..132859..1195741.10761679...
%e A238339 1.21.221..2221..22221..222221..2222221.22222221...
%p A238339 T:= proc(n, k); if n=1 then 2*k+1 else (2*n^(k+1)-n-1)/(n-1) fi end:
%p A238339 seq(seq(T(n-k, k), k=0..n), n=0..10); # _Georg Fischer_, Oct 14 2023
%Y A238339 Cf. A238303.
%K A238339 easy,nonn,tabl
%O A238339 0,5
%A A238339 _Philippe Deléham_, Feb 24 2014
%E A238339 Definition amended by _Georg Fischer_, Oct 14 2023