A103286 Triangle, read by rows, where row n+1 is formed by sorting, in ascending order, the result of the convolution of row n with {2,1}.
1, 1, 2, 2, 2, 5, 4, 5, 6, 12, 8, 12, 14, 17, 30, 16, 30, 32, 40, 48, 77, 32, 76, 77, 94, 112, 136, 202, 64, 184, 202, 230, 265, 318, 384, 540, 128, 432, 540, 588, 662, 760, 901, 1086, 1464, 256, 992, 1464, 1512, 1716, 1912, 2182, 2562, 3073, 4014, 512, 2240
Offset: 0
Examples
Convolution of row 4 {4,5,6,12} with {2,1} = {8,14,17,30,12};
sort to obtain row 5: {8,12,14,17,30}.
Rows begin:
1,
1,2,
2,2,5,
4,5,6,12,
8,12,14,17,30,
16,30,32,40,48,77,
32,76,77,94,112,136,202,
64,184,202,230,265,318,384,540,
128,432,540,588,662,760,901,1086,1464,
256,992,1464,1512,1716,1912,2182,2562,3073,4014,...
Programs
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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]=2*A[k][1];B[k+1]=A[k][k]; for(i=2,k,B[i]=2*A[k][i]+A[k][i-1]); A[k+1]=vecsort(B));return(A[n+1][k+1])}
Comments