cp's OEIS Frontend

A237045 Number of overcompositions of n minus the number of overpartitions of n.

%I A237045 #22 Feb 17 2014 23:42:28
%S A237045 0,0,0,4,12,36,104,260,628,1448,3344,7464,16564,36180,78480,169232,
%T A237045 362732,774172,1645508,3485788,7360208,15503432,32571360,68289536,
%U A237045 142880552,298417848,622194236,1295266596,2692514348,5589496748,11588789220,23998902548
%N A237045 Number of overcompositions of n minus the number of overpartitions of n.
%C A237045 Number of overcompositions of n that contain at least two parts in increasing order.
%F A237045 a(n) = A236002(n) - A015128(n).
%e A237045 Illustration of a(4) = -6 with both overcompositions and overpartitions in colexicographic order.
%e A237045 --------------------------------------------------------
%e A237045 .    Overcompositions of 4      Overpartitions of 4
%e A237045 --------------------------------------------------------
%e A237045 .    _ _ _ _                    _ _ _ _
%e A237045 1   |.| | | |  1', 1,  1,  1   |.| | | |  1', 1,  1,  1
%e A237045 2   |_| | | |  1,  1,  1,  1   |_| | | |  1,  1,  1,  1
%e A237045 3   |  .|.| |  2', 1', 1       |  .|.| |  2', 1', 1
%e A237045 4   |   |.| |  2,  1', 1       |   |.| |  2,  1', 1
%e A237045 5   |  .| | |  2', 1,  1       |  .| | |  2', 1,  1
%e A237045 6   |_ _| | |  2,  1,  1       |_ _| | |  2,  1,  1
%e A237045 7  *|.|  .| |  1', 2', 1       |    .|.|  3', 1
%e A237045 8  *| |  .| |  1,  2', 1       |     |.|  3,  1
%e A237045 9  *|.|   | |  1', 2,  1       |    .| |  3', 1
%e A237045 10 *|_|   | |  1,  2,  1       |_ _ _| |  3,  1
%e A237045 11  |    .|.|  3', 1'          |  .|   |  2', 2
%e A237045 12  |     |.|  3,  1'          |_ _|   |  2,  2
%e A237045 13  |    .| |  3', 1           |      .|  4'
%e A237045 14  |_ _ _| |  3,  1           |_ _ _ _|  4
%e A237045 15 *|.| |  .|  1', 1,  2'
%e A237045 16 *| | |  .|  1,  1,  2'
%e A237045 17 *|.| |   |  1', 1,  2
%e A237045 18 *|_| |   |  1,  1,  2
%e A237045 19  |  .|   |  2', 2
%e A237045 20  |_ _|   |  2,  2
%e A237045 21 *|.|    .|  1', 3'
%e A237045 22 *| |    .|  1,  3'
%e A237045 23 *|.|     |  1', 3
%e A237045 24 *|_|     |  1,  3
%e A237045 25  |      .|  4'
%e A237045 26  |_ _ _ _|  4
%e A237045 .
%e A237045 There are 26 overcompositions of 4 and there are 14 overpartitions of 4, so the difference is a(4) = 26 - 14 = 12.
%e A237045 On the other hand there are 12 overcompositions of 4 that contain at least two parts in increasing order, so a(4) = 12.
%Y A237045 Cf. A000041, A011782, A015128, A056823, A230441, A236002, A236633, A237044, A237047, A237272.
%K A237045 nonn
%O A237045 0,4
%A A237045 _Omar E. Pol_, Feb 02 2014