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Sum of parts that are visible in one of the three views of the shell model of partitions version "tree" with n shells.
4

%I #25 Mar 30 2012 17:34:06

%S 0,1,4,8,15,23,40,59,92,137,202,285,418,577,802,1106,1511,2019,2724,

%T 3598,4755,6226,8107,10462,13523,17280,22029,27953,35350,44416,55763,

%U 69579,86634,107459,132914,163768,201475,246841,301822,368033,447790,543206

%N Sum of parts that are visible in one of the three views of the shell model of partitions version "tree" with n shells.

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

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

%e Illustration of one of the three views with seven shells:

%e .

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

%e . . . . . 1 . . . .

%e . . . . 2 1 . . . .

%e . Table 2.0 . 3 . . 1 2 . . . Table 2.1

%e . . . 2 2 1 . . 3 .

%e . . . . . 1 2 2 . .

%e . 1 . . . .

%e . A182742 A182982 A182743 A182983

%e . A182992 A182994 A182993 A182995

%e .

%e 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.

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

%K nonn

%O 0,3

%A _Omar E. Pol_, Jan 27 2012