A224798 Triangle T, read by rows, where the matrix square T^2 results in shifting T right one column to drop the secondary diagonal (which consists of powers of 2).

1, 1, 1, 4, 2, 1, 24, 8, 4, 1, 224, 64, 16, 8, 1, 3200, 768, 192, 32, 16, 1, 70144, 15360, 2816, 640, 64, 32, 1, 2394112, 454656, 84992, 10752, 2304, 128, 64, 1, 127279104, 22528000, 3223552, 534528, 41984, 8704, 256, 128, 1, 10863804416, 1646198784, 247250944, 24158208, 3706880, 165888, 33792, 512, 256, 1

Offset

0,4

Links

Table of n, a(n) for n=0..54.

Example

Triangle T begins:
1;
1, 1;
4, 2, 1;
24, 8, 4, 1;
224, 64, 16, 8, 1;
3200, 768, 192, 32, 16, 1;
70144, 15360, 2816, 640, 64, 32, 1;
2394112, 454656, 84992, 10752, 2304, 128, 64, 1;
127279104, 22528000, 3223552, 534528, 41984, 8704, 256, 128, 1;
10863804416, 1646198784, 247250944, 24158208, 3706880, 165888, 33792, 512, 256, 1; ...
Illustrate recurrence by products of row and column vectors:
T(4,1) = [16,8,1]*[1,4,16]~ = 16*1 + 8*4 + 1*16 = 64;
T(6,0) = [15360,2816,640,64,32,1]*[1,2,8,64,768,15360]~ = 70144;
T(7,1) = [84992,10752,2304,128,64,1]*[1,4,16,192,2816,84992]~ = 454656.
The matrix square T^2 begins:
1;
2, 1;
10, 4, 1;
72, 24, 8, 1;
768, 224, 64, 16, 1;
12288, 3200, 768, 192, 32, 1;
299008, 70144, 15360, 2816, 640, 64, 1;
11255808, 2394112, 454656, 84992, 10752, 2304, 128, 1;
664469504, 127279104, 22528000, 3223552, 534528, 41984, 8704, 256, 1;
62483333120, 10863804416, 1646198784, 247250944, 24158208, 3706880, 165888, 33792, 512, 1; ...
which equals T shifted right one column with the secondary diagonal dropped.

Prog

(PARI) T(n, k)=if(n<k || k<0, 0, if(n==k, 1, if(n==k+1, 2^(n-1), sum(j=k+1, n, T(n, j)*T(j, k+1) ))))
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

Crossrefs

Cf. A152391, A224799, A224800, A224801, A224802.

Sequence in context: A039948 A111536 A111559 * A239894 A152406 A105623

Adjacent sequences: A224795 A224796 A224797 * A224799 A224800 A224801

Keyword

tabl,nonn

Author

Paul D. Hanna, Apr 22 2013

Status

approved