A182995
Sum of parts of the n-th subsection of the head of the last section of the set of partitions of any odd integer >= 2n+1.
Original entry on oeis.org
3, 7, 18, 44, 82, 158, 303, 507, 873, 1470, 2354, 3756, 5923, 9065, 13815, 20824, 30853, 45365, 66210, 95415, 136696, 194414, 274057, 384136, 535219, 740559, 1019529, 1396212, 1901533, 2577918, 3479291, 4673711, 6253003, 8332767
Offset: 1
a(5)=82 because the 5th subsection of the head of the last section of any odd integer >= 11 looks like this:
(11 . . . . . . . . . . )
( 6 . . . . . 5 . . . . )
( 7 . . . . . . 4 . . . )
( 8 . . . . . . . 3 . . )
( 4 . . . 4 . . . 3 . . )
( 5 . . . . 3 . . 3 . . )
. (2 . )
. (2 . )
. (2 . )
. (2 . )
. (2 . )
. (2 . )
. (2 . )
. (2 . )
There are 21 parts whose sum is 11+6+5+7+4+8+3+4+4+3+5+3+3+2+2+2+2+2+2+2+2 = 11*6 + 2*8 = 82, so a(5) = 82.
a(17) corrected and more terms from Omar E. Pol, Mar 03 2011.
A182813
Triangle read by rows in which row n lists the parts of the largest subshell of all partitions of 2n+1 that do not contain 1 as a part.
Original entry on oeis.org
3, 5, 2, 7, 4, 3, 2, 2, 9, 5, 4, 6, 3, 3, 3, 3, 2, 2, 2, 2, 11, 6, 5, 7, 4, 8, 3, 4, 4, 3, 5, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 13, 7, 6, 8, 5, 9, 4, 5, 4, 4, 10, 3, 5, 5, 3, 6, 4, 3, 7, 3, 3, 4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
Offset: 1
For n=1 the unique partition of 2n+1=3 that does not contains 1 as part is 3, so row 1 has an element = 3.
For n=2 there are 2 partitions of 2n+1=5 that do not contain 1 as part:
5 ............ or ....... 5 . . . .
3 + 2 ........ or .......(3). . 2 .
These partitions contain (3), the row n-1 of triangle, so
the parts of the largest subshell are 5, 2.
For n=3 there are 4 partitions of 2n+1=7 that do not contain 1 as part:
7 ............ or ....... 7 . . . . . .
4 + 3 ........ or ....... 4 . . . 3 . .
5 + 2 ........ or .......(5). . . . 2 .
3 + 2 + 2 .... or .......(3). .(2). 2 .
These partitions contain (5) and (3),(2), the parts of the rows < n of triangle, so the parts of the largest subshell are 7, 4, 3, 2, 2.
And so on.
Triangle begins:
3,
5,2,
7,4,3,2,2,
9,5,4,6,3,3,3,3,2,2,2,2,
11,6,5,7,4,8,3,4,4,3,5,3,3,2,2,2,2,2,2,2,2,
Showing 1-2 of 2 results.
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