A194451 - OEIS

%I #15 Dec 01 2013 13:36:34

%S 1,1,2,2,3,3,5,4,7,5,11,6,15,7,22,8,30,9,42,10,56,11,77,12,101,13,135,

%T 14,176,15,231,16,297,17,385,18,490,19,627,20,792,21,1002,22,1255,23,

%U 1575,24,1958,25,2436,26,3010,27,3718,28,4565,29,5604,30

%N Partition numbers of positive integers and positive integers interleaved.

%C First differences of A194450. The length of the edges in a rectangular spiral whose vertices are the numbers A194450. The spiral contains exactly between its edges the successive last sections of the partitions of the natural numbers. For more information see A135010 and A138121.

%F a(2n-1) = p(n), a(2n) = n.

%F a(2n-1) = A000041(n), a(2n) = A000027(n).

%F a(2n-1) + a(2n) = A133041(n).

%F a(2n-1) - a(2n) = A000094(n+1).

%F a(2n-1) * a(2n) = A066186(n).

%Y Cf. A000041, A194450.

%K nonn

%O 1,3

%A _Omar E. Pol_, Nov 01 2011