%I A025581
%S A025581 0,1,0,2,1,0,3,2,1,0,4,3,2,1,0,5,4,3,2,1,0,6,5,4,3,2,1,0,7,6,5,4,3,2,1,
               0,
%T A025581 8,7,6,5,4,3,2,1,0,9,8,7,6,5,4,3,2,1,0,10,9,8,7,6,5,4,3,2,1,0,11,10,9,
               8,
%U A025581 7,6,5,4,3,2,1,0,12,11,10,9,8,7,6,5,4,3,2,1,0,13,12,11,10,9,8,7,6,5,4,
               3
%N A025581 Triangle T(n,k) = n-k, n >= 0, 0<=k<=k. Integers m to 0 followed by integers 
               m+1 to 0 etc.
%C A025581 The PARI functions t1, t2 can be used to read a square array T(n,k) (n 
               >= 0, k >= 0) by antidiagonals upwards: n -> T(t1(n), t2(n)). - Michael 
               Somos, Aug 23, 2002
%H A025581 M. Somos, <a href="a073189.txt">Sequences used for indexing triangular 
               or square arrays</a>
%F A025581 a(n) = (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n) # Cf. A002262
%F A025581 G.f.: y / [(1-x)^2 * (1-xy) ]. - R. Stephan, Jan 25 2005
%e A025581 0; 1,0; 2,1,0; 3,2,1,0; 4,3,2,1,0; ...
%p A025581 A025581 := n -> binomial(1+floor((1/2)+sqrt(2*(1+n))),2) - (n+1);
%o A025581 (PARI) a(n)=binomial(1+floor(1/2+sqrt(2+2*n)),2)-(n+1) /* produces a(n) 
               */
%o A025581 (PARI) t1(n)=binomial(floor(3/2+sqrt(2+2*n)),2)-(n+1) /* A025581 */
%o A025581 (PARI) t2(n)=n-binomial(floor(1/2+sqrt(2+2*n)),2) /* A002262 */
%Y A025581 A004736(n+1)=1+A025581(n)
%Y A025581 Cf. A025669, A025676, A025683, A002262, A004736.
%Y A025581 Sequence in context: A117901 A074984 A112658 this_sequence A025669 A025676 
               A025683
%Y A025581 Adjacent sequences: A025578 A025579 A025580 this_sequence A025582 A025583 
               A025584
%K A025581 nonn,tabl,easy,nice
%O A025581 0,4
%A A025581 David W. Wilson (davidwwilson(AT)comcast.net)