A154696 - OEIS

A154696

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, 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

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:

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