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A164948 Fibonacci matrix read by antidiagonals. (Inverse of A136158.) 1
1, 1, -1, 3, -4, 1, 9, -15, 7, -1, 27, -54, 36, -10, 1, 81, -189, 162, -66, 13, -1, 243, -648, 675, -360, 105, -16, 1, 729, -2187, 2673, -1755, 675, -153, 19, -1, 2187, -7290, 10206, -7938, 3780, -1134, 210, -22, 1, 6561, -24057, 37908, -34020, 19278, -7182, 1764, -276, 25, -1, 19683, -78732, 137781, -139968, 91854, -40824, 12474, -2592, 351, -28, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

As a triangle, rows sum up to A000007. Diagonals sum up to A001519.

Triangle, read by rows, given by [1,2,0,0,0,0,0,0,0,...] DELTA [-1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Sep 02 2009

Row n: Expansion of (1-x)*(3-x)^(n-1), n>0. - Philippe Deléham, Oct 09 2011

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n,k) = 3*T(n-1,k) - T(n-1,k-1) with T(0,0)=1, T(1,0)=1, T(1,1)=-1. - Philippe Deléham, Oct 09 2011

G.f.: (1-2*x)/(1-3*x+x*y). - R. J. Mathar, Aug 12 2015

EXAMPLE

As triangle:

    1;

    1,   -1;

    3,   -4,    1;

    9,  -15,    7,   -1;

   27,  -54,   36,  -10,    1;

   81, -189,  162,  -66,   13,   -1;

  243, -648,  675, -360,  105,  -16,    1;

CROSSREFS

Cf. A001519, A038763, A136158, A164942.

Sequence in context: A158076 A010611 A136158 * A102051 A078068 A054649

Adjacent sequences:  A164945 A164946 A164947 * A164949 A164950 A164951

KEYWORD

tabl,sign

AUTHOR

Mark Dols, Sep 01 2009

EXTENSIONS

More terms from Philippe Deléham, Oct 09 2011

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)