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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 15:49 EDT 2017. Contains 285329 sequences.