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Riordan array (1/(1-x-x^2), x*(1+2*x)).
0

%I #13 Mar 06 2013 13:07:46

%S 1,1,1,2,3,1,3,4,5,1,5,7,10,7,1,8,11,15,20,9,1,13,18,25,35,34,11,1,21,

%T 29,40,55,75,52,13,1,34,47,65,90,125,143,74,15,1,55,76,105,145,200,

%U 275,247,100,17,1

%N Riordan array (1/(1-x-x^2), x*(1+2*x)).

%C First column is A000045 (Fibonacci numbers) starting with 1.

%C Second column is A000032 (Lucas numbers) starting with 1.

%F T(n,0) = T(n-1,0) + T(n-2,0), T(n,k) = T(n-1,k-1) + 2*T(n-2,k-1) for k>0.

%F Sum_{k, 0<=k<=n} T(n,k) = A094687(n+2).

%F T(2n,n) = A081567(n).

%e Triangle begins

%e 1

%e 1, 1

%e 2, 3, 1

%e 3, 4, 5, 1

%e 5, 7, 10, 7, 1

%e 8, 11, 15, 20, 9, 1

%e 13, 18, 25, 35, 34, 11, 1

%e 21, 29, 40, 55, 75, 52, 13, 1

%e 34, 47, 65, 90, 125, 143, 74, 15, 1

%e 55, 76, 105, 145, 200, 275, 247, 100, 17, 1

%e ...

%e Production array begins

%e 1, 1

%e 1, 2, 1

%e -2, -4, 2, 1

%e 8, 16, -4, 2, 1

%e -40, -80, 16, -4, 2, 1

%e 224, 448, -80, 16, -4, 2, 1

%e -1344, -2688, 448, -80, 16, -4, 2, 1

%e 8448, 16896, -2688, 448, -80, 16, -4, 2, 1

%e ... which is based on A052701.

%Y Cf. A000032, A000045, A002522, A005408, A104726, A123265

%K nonn,tabl

%O 0,4

%A _Philippe Deléham_, Mar 06 2013