A096322 Limiting sequence formed by rows of A094504 read backwards: rightmost floor(n/2)+1 terms of row n in table A094504.

1, 3, 9, 25, 66, 165, 402, 943, 2163, 4835, 10598, 22785, 48215, 100470, 206620, 419662, 842928, 1675487, 3298688, 6436210, 12453352, 23905923, 45550529, 86180937, 161964145, 302447657

Offset: 1

Author

Wouter Meeussen, Jun 27 2004

Keywords

• nonn
• hard
• more

Comments

Same sequence, multiplied by four, occurs in A096272.

a(n) is the number of solid partitions with layer structure an integer partition of (2n-2) in exactly (n-1) parts. - Wouter Meeussen, Mar 12 2025

Examples

			For n=3 the a(3)= 9 solid partitions are generated by the integer partitions of (2n-2) in exactly (n-1) parts with parts =1 and duplicate parts deleted, so just {3} and {2} :
 z[{{3}}], z[{{2,1}}], z[{{1,1,1}}], z[{{2},{1}}], z[{{1,1},{1}}], z[{{1},{1},{1}}] and  z[{{2}}], z[{{1,1}}], z[{{1},{1}}]
		

Links

• Wouter Meeussen, Mma functions for plane and solid partitions

Crossrefs

Cf. A000293, A094504, A094508, A096272, A096573, A096574, A096575, A096576, A096577, A096578, A096579, A096580, A096581.

Extensions

Extended to n=26, Wouter Meeussen, May 23 2025