1,2

The first array is described in A126442 and is the hook case. Sequence A129305 encodes the multisets counted by A096443 and A129306.

a(11) = 9 because 2+2= 4 starting a new array. The arrays begin as follows:

1.....2.....3.....5......7......11.....15.....22

......2.....4.....7......12.....19.....30.....45

............5.....11.....21.....38.....64.....105

..................15.....36.....74.....141.....250

.........................52.....135.....296.....592

................................203....566.....1315

........................................877.....2610

................................................4140

..................9......16.....29.....47.......77

.........................26.....52.....98.....171

................................92.....198.....392

.......................................371.....850

..............................................1663

................................31.....57.....97

.......................................109.....212

..............................................444

...............................66.....137.....269

......................................249.....560

.............................................1075

.............................................109

.............................................300

.............................................712

which sums to

1.....4....12....47....170....750....3255.....16010

Cf. A000041 A035310 A035341 A053445 A060243 A082775 A093802 A096443 A126442 A129305.

Sequence in context: A015755 A096443 A126442 this_sequence A114094 A093936 A119353

Adjacent sequences: A129303 A129304 A129305 this_sequence A129307 A129308 A129309

nonn

Alford Arnold (Alford1940(AT)aol.com), May 07 2007