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A154797 Odd partition numbers of even numbers.

%I A154797 #19 Oct 05 2024 14:34:02
%S A154797 1,5,11,77,135,231,385,627,1575,8349,17977,26015,75175,147273,281589,
%T A154797 386155,526823,966467,3087735,5392783,9289091,20506255,44108109,
%U A154797 56634173,72533807,241265379,304801365,952050665,1482074143,6620830889
%N A154797 Odd partition numbers of even numbers.
%C A154797 Odd numbers in A058696.
%H A154797 Alois P. Heinz, <a href="/A154797/b154797.txt">Table of n, a(n) for n = 1..1000</a>
%e A154797 The odd number 5 is in the sequence as the partition number of the even number 4: (4, 3+1, 2+2, 2+1+1, 1+1+1+1). - _Emeric Deutsch_, Aug 02 2009
%p A154797 aa:= proc(n, i) if n=0 then 1 elif n<0 or i=0 then 0 else aa(n,i):= aa(n, i-1) +aa(n-i, i) fi end: a:= proc(n) local k; if n>1 then a(n-1) fi; for k from `if`(n=1, 0, b(n-1)+2) by 2 while irem(aa(k, k), 2)=0 do od; b(n):= k; aa(k, k) end: seq(a(n), n=1..40); # _Alois P. Heinz_, Jul 28 2009
%p A154797 with(combinat): a := proc (n) if `mod`(numbpart(2*n), 2) = 1 then numbpart(2*n) else end if end proc: seq(a(n), n = 0 .. 70); # _Emeric Deutsch_, Aug 02 2009
%t A154797 Select[PartitionsP[2*Range[0,100]],OddQ] (* _Harvey P. Dale_, Nov 30 2014 *)
%Y A154797 Cf. A000041, A005843, A058696, A154795, A154796, A154798.
%K A154797 nonn
%O A154797 1,2
%A A154797 _Omar E. Pol_, Jan 26 2009
%E A154797 More terms from _Alois P. Heinz_, Jul 28 2009