Search: id:A063967
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%I A063967
%S A063967 1,1,1,2,3,1,3,7,5,1,5,15,16,7,1,8,30,43,29,9,1,13,58,104,95,46,11,1,
%T A063967 21,109,235,271,179,67,13,1,34,201,506,705,591,303,92,15,1,55,365,1051,
%U A063967 1717,1746,1140,475,121,17,1,89,655,2123,3979,4759,3780,2010,703,154
%N A063967 Triangle with a(n,k) = a(n-1,k) + a(n-2,k) + a(n-1,k-1) + a(n-2,k-1) 
               and a(0,0) = 1.
%C A063967 Riordan array (1/(1-x-x^2), (1+x)/(1-x-x^2)). The inverse of the signed 
               version (1/(1+x-x^2),x(1-x)/(1+x-x^2)) is abs(A091698). - Paul Barry 
               (pbarry(AT)wit.ie), Jun 10 2005
%C A063967 Diagonal sums are A002478. - Paul Barry (pbarry(AT)wit.ie), Nov 09 2005
%C A063967 A026729*A007318 as infinite lower triangular matrices . [From Philippe 
               DELEHAM (kolotoko(AT)wanadoo.fr), Dec 11 2008]
%F A063967 G.f.: 1/(1-x*(1+x)*(1+y)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 
               11 2003
%F A063967 T(n, k)=sum{j=0..n, C(j, n-j)C(j, k)}; - Paul Barry (pbarry(AT)wit.ie), 
               Nov 09 2005
%F A063967 Sum_{k, 0<=k<=n}x^k*T(n,k)= (-1)^n*A057086(n), (-1)^n*A057085(n+1), (-1)^n*A057084(n), 
               (-1)^n*A030240(n), (-1)^n*A030192(n), (-1)^n*A030191(n), (-1)^n*A001787(n+1), 
               A000748(n), A108520(n), A049347(n), A000007(n), A000045(n), A002605(n), 
               A030195(n+1), A057087(n), A057088(n), A057089(n), A057090(n), A057091(n), 
               A057092(n), A057093(n), for x = -11, -10, -9, -8, -7, -6, -5, -4, 
               -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 03 2006
%e A063967 Rows start (1), (1,1), (2,3,1), (3,7,5,1), etc. a(3,1)=a(2,1)+a(1,1)+a(2,
               0)+a(1,0)=3+1+2+1=7.
%Y A063967 Columns include A000045 and A023610. Right hand columns include A000012 
               and A005408. Row sums are A002605.
%Y A063967 Matrix inverse: A091698. Matrix square: A091700.
%Y A063967 Columns 0-1: A000045(n+1), A023610(n-1). Main diagonal: A000012. a(n, 
               n-1) = A005408(n-1).
%Y A063967 Row sums are A002605.
%Y A063967 Sequence in context: A158498 A113592 A136555 this_sequence A059397 A152821 
               A071943
%Y A063967 Adjacent sequences: A063964 A063965 A063966 this_sequence A063968 A063969 
               A063970
%K A063967 easy,nonn,tabl
%O A063967 0,4
%A A063967 Henry Bottomley (se16(AT)btinternet.com), Sep 05 2001

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