%I A039823
%S A039823 1,2,4,6,8,11,15,19,23,28,34,40,46,53,61,69,77,86,96,106,116,127,139,
%T A039823 151,163,176,190,204,218,233,249,265,281,298,316,334,352,371,391,411,
%U A039823 431,452,474,496,518,541,565,589,613,638,664,690,716,743,771,799,827
%N A039823 Ceiling[ (n^2+n+2)/4 ].
%C A039823 Equals number of different coefficient values in expansion of Product 
               (1+q^1+...+q^i), i=1 to n. Proof by Lawrence Sze: The Gaussian polynomial 
               Prod[k=1..n, Sum[j=0..k, q^j]] is the q-version of n! and strictly 
               unimodal with constant term 1. It has degree Sum[k=1..n, k]=n(n+1)/
               2 and thus n(n+1)/2+1 nonzero terms.
%F A039823 [ C(n+1, 2)/2 ] + 1.
%F A039823 G.f.: x(x^4-2x^3+2x^2-x+1)/[(1+x^2)(1-x)^3].
%Y A039823 Equals A011848(n+1) + 1.
%Y A039823 Sequence in context: A032514 A011858 A084627 this_sequence A079972 A164144 
               A071241
%Y A039823 Adjacent sequences: A039820 A039821 A039822 this_sequence A039824 A039825 
               A039826
%K A039823 nonn
%O A039823 1,2
%A A039823 Olivier Gerard (olivier.gerard(AT)gmail.com)
%E A039823 Edited by Ralf Stephan, Nov 15 2004