A062189 a(n) = 2 * 3^(n-2)*n*(1+2*n).

0, 2, 20, 126, 648, 2970, 12636, 51030, 198288, 747954, 2755620, 9959598, 35429400, 124357194, 431530092, 1482720390, 5050815264, 17075199330, 57338232372, 191385721566, 635369601960, 2099044209402, 6903833113980

Offset: 0

Author

Henry Bottomley, Jun 13 2001

Keywords

• nonn
• easy

Comments

Define a triangle with left (first) column T(n,0)=n^2 for n=0,1,2,3.. and the remaining terms T(r,c) = T(r-1,c-1) + 2*T(r,c-1). Then T(n,n) = a(n) on the diagonal. T(n,1) = A056105(n). - J. M. Bergot, Jan 26 2013

Links

• Harry J. Smith, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (9,-27,27).

Programs

GAP

List([0..30], n-> 2*3^(n-2)*n*(1+2*n)); # G. C. Greubel, Jun 06 2019

Magma

[2*3^(n-2)*n*(1+2*n): n in [0..30]]; // G. C. Greubel, Jun 06 2019

Mathematica

Table[2*3^(n-2)*n*(1+2*n), {n,0,30}] (* G. C. Greubel, Jun 06 2019 *)
LinearRecurrence[{9,-27,27},{0,2,20},30] (* Harvey P. Dale, Jun 08 2022 *)

PARI

{ for (n=0, 200, write("b062189.txt", n, " ", n*(4*n + 2)*3^(n - 2)) ) } \\ Harry J. Smith, Aug 02 2009

Sage

[2*3^(n-2)*n*(1+2*n) for n in (0..30)] # G. C. Greubel, Jun 06 2019

Formula

a(n) = A002943(n)*A000244(n-2). Binomial transform of A007758.

G.f.: 2*x*(1+x)/(1-3*x)^3. - Ralf Stephan, Mar 13 2003

a(n) = 2*A077616(n). - R. J. Mathar, Jan 29 2013

E.g.f.: 2*x*(1+2*x)*exp(3*x). - G. C. Greubel, Jun 06 2019