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A103284 Triangle, read by rows, where row n+1 is formed by sorting, in ascending order, the result of the convolution of row n with {1,1}.

%I A103284 #6 Nov 19 2015 16:28:10
%S A103284 1,1,1,1,1,2,1,2,2,3,1,3,3,4,5,1,4,5,6,7,9,1,5,9,9,11,13,16,1,6,14,16,
%T A103284 18,20,24,29,1,7,20,29,30,34,38,44,53,1,8,27,49,53,59,64,72,82,97,1,9,
%U A103284 35,76,97,102,112,123,136,154,179,1,10,44,111,173,179,199,214,235,259
%N A103284 Triangle, read by rows, where row n+1 is formed by sorting, in ascending order, the result of the convolution of row n with {1,1}.
%C A103284 Main diagonal is A103285.
%H A103284 Reinhard Zumkeller, <a href="/A103284/b103284.txt">Rows n = 0..125 of triangle, flattened</a>
%F A103284 Row(n+1) = union of {1} and {T(n,k-1) + T(n,k): k=1..n}, sorted in ascending order. - _Reinhard Zumkeller_, Nov 19 2015
%e A103284 Convolution of row 5 {1,4,5,6,7,9} with {1,1} = {1,5,9,11,13,16,9}; sort to obtain row 6: {1,5,9,9,11,13,16}.
%e A103284 Rows begin:
%e A103284 1,
%e A103284 1,1,
%e A103284 1,1,2,
%e A103284 1,2,2,3,
%e A103284 1,3,3,4,5,
%e A103284 1,4,5,6,7,9,
%e A103284 1,5,9,9,11,13,16,
%e A103284 1,6,14,16,18,20,24,29,
%e A103284 1,7,20,29,30,34,38,44,53,
%e A103284 1,8,27,49,53,59,64,72,82,97,
%e A103284 1,9,35,76,97,102,112,123,136,154,179,...
%o A103284 (PARI) {T(n,k)=local(A=vector(n+1,i,vector(i)),B);A[1][1]=1; for(k=1,n,B=vector(k+1);B[1]=1;B[k+1]=A[k][k]; for(i=2,k,B[i]=A[k][i]+A[k][i-1]); A[k+1]=vecsort(B));return(A[n+1][k+1])}
%o A103284 (Haskell)
%o A103284 import Data.List (sort)
%o A103284 a103284 n k = a103284_tabl !! n !! k
%o A103284 a103284_row n = a103284_tabl !! n
%o A103284 a103284_tabl = iterate (\xs -> sort $ zipWith (+) (xs++[0]) ([0]++xs)) [1]
%o A103284 -- _Reinhard Zumkeller_, Nov 19 2015
%Y A103284 Cf. A103285.
%Y A103284 Cf. A000079 (row sums), A257641 (central terms), A257646, A107430.
%K A103284 nonn,tabl
%O A103284 0,6
%A A103284 _Paul D. Hanna_, Jan 28 2005