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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A153656 A row sum 23^n triangular recursion sequence:Prime[j]=23=scale; A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (2*j+3)*Prime[j]*A(n - 2, k - 1). 0
2, 23, 23, 2, 1054, 2, 2, 12165, 12165, 2, 2, 13133, 533412, 13133, 2, 2, 14101, 6422240, 6422240, 14101, 2, 2, 15069, 12779580, 270482476, 12779580, 15069, 2, 2, 16037, 19605432, 3385203976, 3385203976, 19605432, 16037, 2, 2, 17005, 26899796 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

First version was wrong: the j function increases with larger j.

Row sums are:

{2, 46, 1058, 24334, 559682, 12872686, 296071778, 6809650894, 156621970562,

3602305322926,...}.

Plot of the lowest level of the fractal is:

a = Table[Table[If[m <= n, If[Mod[A[n, m], 23] == 0, 0, 1], 0], {m, 1, 10}], {n, 1, 10}] ;

ListDensityPlot[a, Mesh -> False, Axes -> False]

LINKS

Table of n, a(n) for n=1..39.

FORMULA

A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (2*j+3)*Prime[j]*A(n - 2, k - 1).

EXAMPLE

{2},

{23, 23},

{2, 1054, 2},

{2, 12165, 12165, 2},

{2, 13133, 533412, 13133, 2},

{2, 14101, 6422240, 6422240, 14101, 2},

{2, 15069, 12779580, 270482476, 12779580, 15069, 2},

{2, 16037, 19605432, 3385203976, 3385203976, 19605432, 16037, 2},

{2, 17005, 26899796, 9577346548, 137413443860, 9577346548, 26899796, 17005, 2},

{2, 17973, 34662672, 19073670000, 1782044310816, 1782044310816, 19073670000, 34662672, 17973, 2}

MATHEMATICA

Clear[t, n, m, A, a]; j = 9;

A[2, 1] := A[2, 2] = Prime[j];

A[3, 2] = 2*Prime[j]^2 - 4;

A[4, 2] = A[4, 3] = Prime[j]^3 - 2;

A[n_, 1] := 2; A[n_, n_] := 2;

A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (2*j+3)*Prime[j]*A[n - 2, k - 1];

Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}] ;

Flatten[%] Table[Sum[A[n, m], {m, 1, n}], {n, 1, 10}] ;

Table[Sum[A[n, m], {m, 1, n}]/(2*Prime[j]^(n - 1)), {n, 1, 10}]

CROSSREFS

Sequence in context: A158992 A128365 A153654 * A242037 A233692 A084323

Adjacent sequences:  A153653 A153654 A153655 * A153657 A153658 A153659

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Dec 30 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 May 24 00:38 EDT 2019. Contains 323528 sequences. (Running on oeis4.)