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Search: id:A063967
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| A063967 |
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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. |
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16
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| 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, 21, 109, 235, 271, 179, 67, 13, 1, 34, 201, 506, 705, 591, 303, 92, 15, 1, 55, 365, 1051, 1717, 1746, 1140, 475, 121, 17, 1, 89, 655, 2123, 3979, 4759, 3780, 2010, 703, 154
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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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
Diagonal sums are A002478. - Paul Barry (pbarry(AT)wit.ie), Nov 09 2005
A026729*A007318 as infinite lower triangular matrices . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 11 2008]
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FORMULA
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G.f.: 1/(1-x*(1+x)*(1+y)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 11 2003
T(n, k)=sum{j=0..n, C(j, n-j)C(j, k)}; - Paul Barry (pbarry(AT)wit.ie), Nov 09 2005
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
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EXAMPLE
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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.
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CROSSREFS
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Columns include A000045 and A023610. Right hand columns include A000012 and A005408. Row sums are A002605.
Matrix inverse: A091698. Matrix square: A091700.
Columns 0-1: A000045(n+1), A023610(n-1). Main diagonal: A000012. a(n, n-1) = A005408(n-1).
Row sums are A002605.
Sequence in context: A158498 A113592 A136555 this_sequence A059397 A152821 A071943
Adjacent sequences: A063964 A063965 A063966 this_sequence A063968 A063969 A063970
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Sep 05 2001
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