A206800 Riordan array (1/(1-3*x+x^2), x*(1-x)/(1-3*x+x^2)).

1, 3, 1, 8, 5, 1, 21, 19, 7, 1, 55, 65, 34, 9, 1, 144, 210, 141, 53, 11, 1, 377, 654, 534, 257, 76, 13, 1, 987, 1985, 1905, 1111, 421, 103, 15, 1, 2584, 5911, 6512, 4447, 2041, 641, 134, 17, 1, 6765, 17345, 21557, 16837, 9038, 3440, 925, 169, 19, 1

Offset: 0

Author

Philippe Deléham, Feb 12 2012

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins :
1
3, 1
8, 5, 1
21, 19, 7, 1
55, 65, 34, 9, 1
144, 210, 141, 53, 11, 1
377, 654, 534, 257, 76, 13, 1
987, 1985, 1905, 1111, 421, 103, 15, 1
2584, 5911, 6512, 4447, 2041, 641, 134, 17, 1
6765, 17345, 21557, 16837, 9038, 3440, 925, 169, 19, 1
Triangle (0,3,-1/3,1/3,0,0,0,0,0,...) DELTA (1,0,-1/3,1/3,0,0,0,0,...) begins :
1
0, 1
0, 3, 1
0, 8, 5, 1
0, 21, 19, 7, 1
0, 55, 65, 34, 9, 1...
		

References

• 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.
• Antidiagonal sums are A072264(n).

Crossrefs

Cf. A000045, A001519, A001906, A001870,

Formula

T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1).

G.f.: 1/(1-(y+3)*x+(y+1)*x^2).

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.