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A117433 Number of planar partitions of n with all part sizes distinct. 2
1, 1, 1, 3, 3, 5, 9, 11, 15, 21, 35, 41, 59, 75, 103, 149, 187, 243, 321, 413, 527, 735, 895, 1165, 1467, 1885, 2335, 2997, 3853, 4765, 5977, 7473, 9269, 11531, 14255, 17537, 22201, 26897, 33233, 40613, 50027, 60637, 74459, 89963, 109751, 134407, 162117 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Matches A072706 for n < 10, since a unimodal composition into distinct parts can be placed uniquely as a hook. Starting with n = 10, additional partitions are possible (starting with [4,3|2,1] and [4,2|3,1]).

LINKS

Franklin T. Adams-Watters and Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 100 terms from Franklin T. Adams-Watters)

FORMULA

a(n) = sum_{k=1}^{floor((sqrt(8*n+1)-1)/2)} A000085(k)*A008289(n,k).

MAPLE

b:= proc(n, i) b(n, i):= `if`(n=0, [1], `if`(i<1, [], zip((x, y)

      -> x+y, b(n, i-1), `if`(i>n, [], [0, b(n-i, i-1)[]]), 0)))

    end:

g:= proc(n) g(n):= `if`(n<2, 1, (n-1)*g(n-2) +g(n-1)) end:

a:= proc(n) b(n, n); add(%[i]*g(i-1), i=1..nops(%)) end:

seq (a(n), n=0..60);  # Alois P. Heinz, Nov 18 2012

CROSSREFS

Cf. A000219, A072706, A117434, A000009.

Sequence in context: A091916 A102437 A072706 * A159284 A078028 A279375

Adjacent sequences:  A117430 A117431 A117432 * A117434 A117435 A117436

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Mar 16 2006, Apr 01 2008

STATUS

approved

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Last modified July 21 02:47 EDT 2017. Contains 289629 sequences.