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.

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

1,1

Comments

The last section of the set of partitions of 2n+1 contains n subsections.

Also first differences of A182737. - Omar E. Pol, Mar 03 2011

Links

Table of n, a(n) for n=1..34.

Formula

a(n) = A138880(2n+1) - A138880(2n-1).

Example

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.

Crossrefs

Cf. A135010, A138880, A182737, A182743, A182983, A182993, A182994.

Sequence in context: A036670 A369200 A262321 * A027967 A181306 A178035

Adjacent sequences: A182992 A182993 A182994 * A182996 A182997 A182998

Keyword

nonn

Author

Omar E. Pol, Feb 06 2011

Extensions

a(17) corrected and more terms from Omar E. Pol, Mar 03 2011.

a(12) corrected by Georg Fischer, Aug 31 2020

Status

approved