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%I #6 Feb 22 2013 14:40:25
%S 1,3,1,8,5,1,21,19,7,1,55,65,34,9,1,144,210,141,53,11,1,377,654,534,
%T 257,76,13,1,987,1985,1905,1111,421,103,15,1,2584,5911,6512,4447,2041,
%U 641,134,17,1,6765,17345,21557,16837,9038,3440,925,169,19,1
%N Riordan array (1/(1-3*x+x^2), x*(1-x)/(1-3*x+x^2)).
%D Subtriangle of the triangle given by (0, 3, -1/3, 1/3, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -1/3, 1/3, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%D Antidiagonal sums are A072264(n).
%F T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1).
%F G.f.: 1/(1-(y+3)*x+(y+1)*x^2).
%F Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n* A015587(n+1), (-1)^n*A190953(n+1), (-1)^n*A015566(n+1), (-1)*A189800(n+1), (-1)^n*A015541(n+1), (-1)^n*A085939(n+1), (-1)^n*A015523(n+1), (-1)^n*A063727(n), (-1)^n*A006130(n), A077957(n), A000045(n+1), A000079(n), A001906(n+1), A007070(n), A116415(n), A084326(n+1), A190974(n+1), A190978(n+1), A190984(n+1), A190990(n+1), A190872(n) for x = -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8 respectively.
%e Triangle begins :
%e 1
%e 3, 1
%e 8, 5, 1
%e 21, 19, 7, 1
%e 55, 65, 34, 9, 1
%e 144, 210, 141, 53, 11, 1
%e 377, 654, 534, 257, 76, 13, 1
%e 987, 1985, 1905, 1111, 421, 103, 15, 1
%e 2584, 5911, 6512, 4447, 2041, 641, 134, 17, 1
%e 6765, 17345, 21557, 16837, 9038, 3440, 925, 169, 19, 1
%e Triangle (0,3,-1/3,1/3,0,0,0,0,0,...) DELTA (1,0,-1/3,1/3,0,0,0,0,...) begins :
%e 1
%e 0, 1
%e 0, 3, 1
%e 0, 8, 5, 1
%e 0, 21, 19, 7, 1
%e 0, 55, 65, 34, 9, 1...
%Y Cf. A000045, A001519, A001906, A001870,
%K easy,nonn,tabl
%O 0,2
%A _Philippe Deléham_, Feb 12 2012
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