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A119687 f-Pascal's triangle where f(n) = n^2 = A000290(n).

%I A119687 #34 May 12 2020 07:55:28
%S A119687 1,1,1,1,2,1,1,5,5,1,1,26,50,26,1,1,677,3176,3176,677,1,1,458330,
%T A119687 10545305,20173952,10545305,458330,1,1,210066388901,111413523931925,
%U A119687 518191796841329,518191796841329,111413523931925,210066388901,1
%N A119687 f-Pascal's triangle where f(n) = n^2 = A000290(n).
%C A119687 The second diagonal, T(n,n-1) = A003095(n). - _Cortney Reagle_, Sep 17 2019
%H A119687 Cortney Reagle, <a href="/A119687/b119687.txt">Table of n, a(n) for n = 0..104</a> (Rows n = 0..12 of the triangle, flattened)
%F A119687 T(n, k) = T(n-1, k-1)^2 + T(n-1, k)^2; T(0,0) = 1; T(n,-1) = 0; T(n, k) = 0, n < k.
%e A119687 Triangle T(n,k) (with rows n >= 0 and columns 0 <= k <= n) begins as follows:
%e A119687   1;
%e A119687   1,      1;
%e A119687   1,      2,        1;
%e A119687   1,      5,        5,        1;
%e A119687   1,     26,       50,       26,        1;
%e A119687   1,    677,     3176,     3176,      677,      1;
%e A119687   1, 458330, 10545305, 20173952, 10545305, 458330, 1;
%e A119687   ...
%o A119687 (PARI) T(n)={my(M=matrix(n,n)); M[1,1]=1; for(n=2, n, M[n,1]=1; for(k=2, n, M[n,k]=M[n-1,k-1]^2 + M[n-1,k]^2)); M}
%o A119687 { my(A=T(7)); for(i=1, #A, print(A[i,1..i])) } \\ _Andrew Howroyd_, Sep 17 2019
%Y A119687 Row sums are A327563.
%Y A119687 Cf. A007318, A003095.
%K A119687 nonn,tabl
%O A119687 0,5
%A A119687 _Philippe Deléham_, Jun 09 2006
%E A119687 a(12) = 50 inserted and more terms added by _Cortney Reagle_, Sep 17 2019