login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A154696 Generalized Sierpinski-Pascal-MacMahon gasket triangular sequence defined by T(n, m) = (r^(n-m)*q^m + r^m*q^(n-m))*b(n), where b(n) = coefficients of p(x, n) = 2^n*(1-x)^(n+1) * LerchPhi(x, -n, 1/2), and r=2, q=3. 2
2, 5, 5, 13, 72, 13, 35, 690, 690, 35, 97, 5928, 16560, 5928, 97, 275, 49770, 302760, 302760, 49770, 275, 793, 420204, 4934124, 10172736, 4934124, 420204, 793, 2315, 3595350, 76427820, 280500840, 280500840, 76427820, 3595350, 2315 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are: {2, 10, 98, 1450, 28610, 705610, 20882978, 721052650, 28453354370, 1263142915210, 62305874905058, ...}

LINKS

G. C. Greubel, Rows n = 0..40 of triangle, flattened

A. Lakhtakia, R. Messier, V. K. Varadan, V. V. Varadan, Use of combinatorial algebra for diffusion on fractals, Physical Review A, volume 34, Number 3 (1986) p. 2502, Fig. 3.

FORMULA

Let r = 2 and q = 3 then b(n) = the coefficients of p(x, n) =  2^n*(1 - x)^(n + 1)* LerchPhi(x, -n, 1/2). The triangle is then defined by T(n, m) = (r^(n-m)*q^m + r^m*q^(n-m))*b(n).

EXAMPLE

Triangle begins as:

    2;

    5,      5;

   13,     72,      13;

   35,    690,     690,       35;

   97,   5928,   16560,     5928,      97;

  275,  49770,  302760,   302760,   49770,    275;

  793, 420204, 4934124, 10172736, 4934124, 420204, 793;

MATHEMATICA

r = 2; q = 3; p[x_, n_] = 2^n*(1-x)^(n+1)*LerchPhi[x, -n, 1/2];

b:= Table[CoefficientList[Series[p[x, n], {x, 0, 30}], x], {n, 0, 20}];

T[n_, m_]:= (r^(n-m)*q^m + r^m*q^(n-m))*b[[n+1]][[m+1]];

Table[T[n, m], {n, 0, 12}, {m, 0, n}]//Flatten (* modified by G. C. Greubel, May 08 2019 *)

CROSSREFS

Sequence in context: A183419 A305314 A154694 * A154698 A063786 A121304

Adjacent sequences:  A154693 A154694 A154695 * A154697 A154698 A154699

KEYWORD

nonn,tabl,less

AUTHOR

Roger L. Bagula and Gary W. Adamson, Jan 14 2009

EXTENSIONS

Edited by G. C. Greubel, May 08 2019

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 July 5 15:26 EDT 2020. Contains 335473 sequences. (Running on oeis4.)