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A125693 Riordan array ((1-x)/(1-3*x),x*(1-x)/(1-3*x)). 1
1, 2, 1, 6, 4, 1, 18, 16, 6, 1, 54, 60, 30, 8, 1, 162, 216, 134, 48, 10, 1, 486, 756, 558, 248, 70, 12, 1, 1458, 2592, 2214, 1168, 410, 96, 14, 1, 4374, 8748, 8478, 5160, 2150, 628, 126, 16, 1, 13122, 29160, 31590, 21744, 10442, 3624, 910, 160, 18, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are A001835(n+1). Diagonal sums are A030186. Inverse is A125694. Equal to product of A007318 and A073370.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

Number triangle T(n,k)=sum{j=0..k+1, C(k+1,j)C(n-j,n-k-j)(-1)^j*3^(n-k-j)}

T(n,k)=3*T(n-1,k)+T(n-1,k-1)-T(n-2,k-1), T(0,0)=1, T(1,0)=2, T(1,1)=1, T(n,k)=0 if k>n or if k<n. - Philippe Deléham, Jan 08 2013

EXAMPLE

Triangle begins

1,

2, 1,

6, 4, 1,

18, 16, 6, 1,

54, 60, 30, 8, 1,

162, 216, 134, 48, 10, 1

MATHEMATICA

T[0, 0] = 1; T[1, 0] = 2; T[1, 1] = 1; T[n_, k_] /; 0 <= k <= n := T[n, k] = 3 T[n - 1, k] + T[n - 1, k - 1] - T[n - 2, k - 1]; T[_, _] = 0;

Table[T[n, k], {n, 0, 9}, {k, 0, n}] (* Jean-François Alcover, Jun 13 2019 *)

CROSSREFS

Sequence in context: A118040 A073387 A259099 * A094527 A054335 A110681

Adjacent sequences:  A125690 A125691 A125692 * A125694 A125695 A125696

KEYWORD

nonn,tabl,easy

AUTHOR

Paul Barry, Nov 30 2006

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)