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A317085 Number of integer partitions of n whose sequence of multiplicities is a palindrome.

%I A317085 #16 Jun 29 2020 22:13:41
%S A317085 1,1,2,3,4,4,8,6,11,12,18,16,31,25,40,47,60,58,92,85,125,135,165,173,
%T A317085 248,246,310,351,435,450,602,608,766,846,997,1098,1382,1421,1713,1912,
%U A317085 2272,2413,2958,3118,3732,4135,4718,5127,6170,6550,7638,8396,9667,10433
%N A317085 Number of integer partitions of n whose sequence of multiplicities is a palindrome.
%H A317085 Chai Wah Wu, <a href="/A317085/b317085.txt">Table of n, a(n) for n = 0..166</a>
%H A317085 Wikipedia, <a href="https://en.wikipedia.org/wiki/Palindrome">Palindrome</a>
%e A317085 The a(10) = 18 partitions:
%e A317085 (ten),
%e A317085 (91), (82), (73), (64), (55),
%e A317085 (721), (631), (541), (532),
%e A317085 (5221), (4411), (4321), (3322),
%e A317085 (33211), (32221), (22222),
%e A317085 (1111111111).
%t A317085 Table[Length[Select[IntegerPartitions[n],Length/@Split[#]==Reverse[Length/@Split[#]]&]],{n,30}]
%o A317085 (Python)
%o A317085 from sympy.utilities.iterables import partitions
%o A317085 def A317085(n):
%o A317085     c = 1
%o A317085     for d in partitions(n,m=n*2//3):
%o A317085         l = len(d)
%o A317085         if l > 0:
%o A317085             k = sorted(d.keys())
%o A317085             for i in range(l//2):
%o A317085                 if d[k[i]] != d[k[l-i-1]]:
%o A317085                     break
%o A317085             else:
%o A317085                 c += 1
%o A317085     return c # _Chai Wah Wu_, Jun 22 2020
%Y A317085 Cf. A000041, A000837, A025065, A124010, A242414, A317086, A317087.
%K A317085 nonn
%O A317085 0,3
%A A317085 _Gus Wiseman_, Jul 21 2018