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

0,3

Comments

Row sums are powers of 3. Main diagonal is A103287.

Links

Table of n, a(n) for n=0..56.

Example

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,...

Prog

(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])}

Crossrefs

Cf. A103287, A103284.

Sequence in context: A147293 A134634 A346500 * A285704 A058704 A316660

Adjacent sequences: A103283 A103284 A103285 * A103287 A103288 A103289

Keyword

nonn,tabl

Author

Paul D. Hanna, Jan 28 2005

Status

approved