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A083029 Triangle read by rows: T(n,k), n >=1, 0 <= k <= C(n,k), = number of n X n symmetric positive semi-definite matrices with 2's on the main diagonal and 1's and 0's elsewhere and with k 1's above the diagonal.

%I A083029 #14 Jun 06 2024 08:23:18
%S A083029 1,1,1,1,3,3,1,1,6,15,20,15,6,1,1,10,45,120,210,192,200,90,45,10,1,1,
%T A083029 15,105,455,1365,2517,3805,3975,3690,2910,1548,975,255,105,15,1,1,21,
%U A083029 210,1330,5985,18207,39557,71235,95130,115115,110670,104265,72520,56070,32445,15862,7434,2730,665,210,21,1,1,28,378,3276,20475,91392,288596,692576,1374597,2161180,3247622,3740016,4422915,4117512,3886200,3044048,2579780,1591296,1111768,628600,323148,148184,65576,20160,7105,1540,378,28,1
%N A083029 Triangle read by rows: T(n,k), n >=1, 0 <= k <= C(n,k), = number of n X n symmetric positive semi-definite matrices with 2's on the main diagonal and 1's and 0's elsewhere and with k 1's above the diagonal.
%H A083029 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%e A083029 1;
%e A083029 1,1;
%e A083029 1,3,3,1;
%e A083029 1,6,15,20,15,6,1;
%e A083029 ...
%Y A083029 Rows sums give A085658.
%Y A083029 A038379(n) = Sum_{k=0..C(n,2)} 2^k * T(n,k).
%Y A083029 A084546 is an upper bound.
%K A083029 nonn,tabf
%O A083029 1,5
%A A083029 _N. J. A. Sloane_, Jul 13 2003
%E A083029 Rows n=6..8 added by _Max Alekseyev_, Jun 05 2024