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A204842 Triangle by rows relating to A081696 1
1, 1, 2, 3, 4, 2, 9, 12, 6, 2, 29, 38, 20, 8, 2, 97, 126, 68, 30, 10, 2, 333, 430, 236, 110, 42, 12, 2, 1165, 1498, 832, 402, 166, 56, 14, 2, 4135, 5300, 2970, 1472, 640, 238, 72, 16, 2, 14845, 18980, 10710, 5410, 2440, 968, 328, 90, 18, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

n-th row of the triangle is the top row of M^n, where M is the following infinite square production matrix:

1, 2, 0, 0, 0, 0,...

1, 1, 1, 0, 0, 0,...

1, 1, 1, 1, 0, 0,...

1, 1, 1, 1, 1, 0,...

1, 1, 1, 1, 1, 1,...

...

Conjecture: T(n,1) = 2*A109262(n). T(n,2)=2*A109263(n). - R. J. Mathar, Jul 21 2015

EXAMPLE

First few rows of the triangle =

1;

1, 2;

3, 4, 2;

9, 12, 6, 2;

29, 38, 20, 8, 2;

97, 126, 68, 30, 10, 2;

333, 430, 236, 110, 42, 12, 2;

1165, 1498, 832, 402, 166, 56, 14, 2;

4135, 5300, 2970, 1472, 640, 238, 72, 16, 2;

14845, 18980, 10710, 5410, 2440, 968, 328, 90, 18, 2;

...

Top row of M^3 = [9, 12, 6, 2, 0, 0, 0,...]

MAPLE

A204842T := proc(n, k)

    if n =0 and k =1 then

        2;

    elif k <0 or k >n+1 then

        0;

    else

        1;

    end if ;

end proc:

A204842 := proc(n, k)

    local A;

    A := Matrix(n+1, n+1) ;

    for row from 1 to n+1 do

    for col from 1 to n+1 do

            A[row, col] := A204842T(row-1, col-1) ;

    end do:

    end do:

    Mn := LinearAlgebra[MatrixPower](A , n);

    Mn[1, k+1] ;

end proc:

for n from 0 to 10 do

    for k from 0 to n do

    printf("%d ", A204842(n, k)) ;

    end do:

    printf("\n") ;

end do:

CROSSREFS

Cf. A081696 (first column and also row sums).

Sequence in context: A324911 A220335 A117009 * A103300 A305402 A213394

Adjacent sequences:  A204839 A204840 A204841 * A204843 A204844 A204845

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jan 19 2012

STATUS

approved

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Last modified November 21 16:04 EST 2019. Contains 329371 sequences. (Running on oeis4.)