%I A008805
%S A008805 1,1,3,3,6,6,10,10,15,15,21,21,28,28,36,36,45,45,55,55,
%T A008805 66,66,78,78,91,91,105,105,120,120,136,136,153,153,171,
%U A008805 171,190,190,210,210,231,231,253,253,276,276,300,300,325
%N A008805 Triangular numbers repeated.
%C A008805 Number of choices for nonnegative integers x,y,z such that x and y are 
               even and x+y+z=n.
%C A008805 a(n) = number of partitions of n+4 such that the differences between 
               greatest and smallest parts are 2: a(n-4)=A097364(n,2) for n>3. - 
               Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 09 2004
%C A008805 a(n) = A108299(n-2,n)*(-1)^floor((n+1)/2) for n>1. - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Jun 01 2005
%D A008805 H. D. Brunk, An Introduction to Mathematical Statistics, Ginn, Boston, 
               1960; p. 360.
%H A008805 <a href="Sindx_Tu.html#2wis">Index entries for two-way infinite sequences</
               a>
%F A008805 a(n)=(2n+5)(-1)^n/16+(2n^2+10n+11)/16; a(n)=sum{k=0..n, ((k+2)(1+(-1)^k))/
               4 }. - Paul Barry (pbarry(AT)wit.ie), May 31 2003
%F A008805 G.f.: 1/((1-x)(1-x^2)^2). E.g.f.: exp(x)(2x^2+12x+11)/16+exp(-x)(-2x+5)/
               16. a(-n)=a(-5+n).
%F A008805 a(n)=sum{k=0..n, floor((k+2)/2)(1-(-1)^(n+k-1))/2}; a(n)=sum{k=0..floor(n/
               2), floor((n-2k+2)/2)}; - Paul Barry (pbarry(AT)wit.ie), Apr 16 2005
%F A008805 A signed version of A008805 is given by sum{k=0..n, (-1)^k floor(k^2/
               4)}. - Paul Barry (pbarry(AT)wit.ie), Aug 19 2003
%F A008805 a(n+1)=[sum{k=1..n, k} mod (n+1)] + a(n), with n>=1 and a(1)=1 - Paolo 
               P. Lava (ppl(AT)spl.at), Mar 19 2007
%p A008805 1/((1-x)*(1-x^2)^2);
%p A008805 a:=n->sum(j, j=0..n/2): seq(a(n), n=2..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 30 2007
%o A008805 (PARI) a(n)=(n\2+2)*(n\2+1)/2
%Y A008805 Diagonal sums of A002260, when arranged as a number triangle. - Paul 
               Barry (pbarry(AT)wit.ie), Feb 28 2003
%Y A008805 Sequence in context: A110261 A049318 A079551 this_sequence A026925 A088528 
               A131942
%Y A008805 Adjacent sequences: A008802 A008803 A008804 this_sequence A008806 A008807 
               A008808
%K A008805 nonn
%O A008805 0,3
%A A008805 N. J. A. Sloane (njas(AT)research.att.com).