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A194804 Sum of parts that are visible in one of the three views of the shell model of partitions version "tree" with n shells. 4
0, 1, 4, 8, 15, 23, 40, 59, 92, 137, 202, 285, 418, 577, 802, 1106, 1511, 2019, 2724, 3598, 4755, 6226, 8107, 10462, 13523, 17280, 22029, 27953, 35350, 44416, 55763, 69579, 86634, 107459, 132914, 163768, 201475, 246841, 301822, 368033, 447790, 543206 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For the number of parts see A194803. For more information about the shell model see A135010 and A194805.

LINKS

Table of n, a(n) for n=0..41.

FORMULA

a(n) = n + A138880(n-1) + A138880(n), if n >= 2.

EXAMPLE

Illustration of one of the three views with seven shells:

.

.        A182732 <- 6 3 4 2 1 3 5 4 7 -> A182733

.                   . . . . 1 . . . .

.                   . . . 2 1 . . . .

.      Table 2.0    . 3 . . 1 2 . . .    Table 2.1

.                   . . 2 2 1 . . 3 .

.                   . . . . 1 2 2 . .

.                           1 . . . .

.  A182742  A182982                   A182743  A182983

.  A182992  A182994                   A182993  A182995

.

The sum of parts that are visible is 1+1+1+1+1+1+1+2+2+2+2+2+2+2+3+3+3+3+4+4+5+6+7 = 59, so a(7) = 59. Using the formula we have a(7) = 7+24+28 = 59.

CROSSREFS

Cf. A002865, A066186, A135010, A138121, A138880, A182732, A182733, A182742, A182743, A182982, A182983, A182992-A182995, A194803, A194805.

Sequence in context: A122247 A126255 A267682 * A169953 A213035 A014146

Adjacent sequences:  A194801 A194802 A194803 * A194805 A194806 A194807

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jan 27 2012

STATUS

approved

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Last modified July 11 05:49 EDT 2020. Contains 335609 sequences. (Running on oeis4.)