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A206306 Riordan array (1, x/(1-3*x+2*x^2)). 1
1, 0, 1, 0, 3, 1, 0, 7, 6, 1, 0, 15, 23, 9, 1, 0, 31, 72, 48, 12, 1, 0, 63, 201, 198, 82, 15, 1, 0, 127, 522, 699, 420, 125, 18, 1, 0, 255, 1291, 2223, 1795, 765, 177, 21, 1, 0, 511, 3084, 6562, 6768, 3840, 1260, 238, 24, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Triangle T(n,k), read by rows, given by (0, 3, -2/3, 2/3, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

Diagonals sums are even indexed Fibonacci numbers.

LINKS

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

FORMULA

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A204089(n), A204091(n) for x = 0, 1, 2 respectively.

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

T(n,n) = 1, T(n+1,n) = 3n = A008585(n), T(n+2,n) = A062725(n).

T(n,k)=3*T(n-1,k)+T(n-1,k-1)-T(n-2,k), T(0,0)=T(1,1)=T(2,2)=1, T(1,0)=T(2,0)=0, T(2,1)=3, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Nov 17 2013

EXAMPLE

Triangle begins :

1

0, 1

0, 3, 1

0, 7, 6, 1

0, 15, 23, 9, 1

0, 31, 72, 48, 12, 1

0, 63, 201, 198, 82, 15, 1

0, 127, 522, 699, 420, 125, 18, 1

0, 255, 1291, 2223, 1795, 765, 177, 21, 1

0, 511, 3084, 6562, 6768, 3840, 1260, 238, 24, 1

0, 1023, 7181, 18324, 23276, 16758, 7266, 1932, 308, 27, 1

CROSSREFS

Cf. Columns : A000007, A000225 (Mersenne numbers), A045618, A055582,

Cf. A110441

Sequence in context: A176108 A110504 A111246 * A178124 A143395 A090536

Adjacent sequences:  A206303 A206304 A206305 * A206307 A206308 A206309

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Feb 06 2012

STATUS

approved

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Last modified April 23 06:16 EDT 2014. Contains 240913 sequences.