login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A152462 A posterior vector Markov of A000045 as a triangular sequence: A back-iterated Markov with M=Inverse[{{0, 1}, {1, 1}}]={{-1, 1}, {1, 0}}; and v(0)={Fibonacci[n],Fibonacci[n-1]}, to give t(n,m)=v(m)=(M^m*v(0))_first_element. (Starting vector symmetrical in n,m.) 0
1, 1, -1, 2, -1, 1, 3, -2, 1, -1, 5, -3, 3, -1, -1, 8, -5, 5, -4, -1, 7, 13, -8, 9, -7, 4, 7, -27, 21, -13, 15, -13, 9, -1, -27, 83, 34, -21, 25, -22, 19, -9, -14, 83, -239, 55, -34, 41, -37, 34, -25, -1, 62, -239, 659, 89, -55, 67, -61, 59, -49, 25, 41, -205, 659, -1781 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The row sums are {1, -1, 8, 17, 115, 412, 1929, 7771, 33908, 141225, 604359, ...}.

This starting vector method gives nonzero low values

and a lower overall triangle.

LINKS

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

FORMULA

A back-iterated Markov with M=Inverse[{{0, 1}, {1, 1}}]={{-1, 1}, {1, 0}};

and v(0)={Fibonacci[n],Fibonacci[n-1]}, to give t(n,m)=v(m)=(M^m*v(0))_first_element.

EXAMPLE

{1},

{1, -1},

{2, -1, 1},

{3, -2, 1, -1},

{5, -3, 3, -1, -1},

{8, -5, 5, -4, -1, 7},

{13, -8, 9, -7, 4, 7, -27},

{21, -13, 15, -13, 9, -1, -27, 83},

{34, -21, 25, -22, 19, -9, -14,83, -239},

{55, -34, 41, -37, 34, -25, -1, 62, -239, 659},

{89, -55, 67, -61, 59, -49, 25, 41, -205, 659, -1781}

MATHEMATICA

Clear[M, a];

M = Inverse[{{0, 1}, {1, 1}}];

a = Table[(MatrixPower[M, n].{1, 0})[[1]], {n, -30, 30}];

Table[Table[(MatrixPower[M, m].{a[[30 - (n - m + 1)]], a[[30 - (m - 1)]]})[[1]], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Cf. A000045.

Sequence in context: A287920 A027293 A104762 * A180360 A318805 A175331

Adjacent sequences:  A152459 A152460 A152461 * A152463 A152464 A152465

KEYWORD

tabl,uned,sign

AUTHOR

Roger L. Bagula, Dec 05 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 16 20:45 EST 2019. Contains 320189 sequences. (Running on oeis4.)