A144843 a(n) = (6^n - 2^n)^2 / 16.

1, 64, 2704, 102400, 3748096, 135675904, 4893282304, 176265625600, 6346852335616, 228502162898944, 8226263614357504, 296147719133593600, 10661344637077159936, 383808727914259677184, 13817118056668205154304, 497416296261117961830400, 17906987220053014721069056

Offset: 1

Author

Al Hakanson (hawkuu(AT)gmail.com), Sep 22 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..630
• Index entries for linear recurrences with constant coefficients, signature (52,-624,1728).

Crossrefs

Cf. A016129.

Programs

Magma

[4^(n-2)*(3^n-1)^2: n in [1..30]]; // G. C. Greubel, Oct 03 2024

Mathematica

Table[(6^n-2^n)^2/16, {n,20}] (* Harvey P. Dale, Apr 15 2020 *)

SageMath

[4^(n-2)*(3^n-1)^2 for n in range(1,31)] # G. C. Greubel, Oct 03 2024

Formula

From R. J. Mathar, Sep 24 2008: (Start)

a(n) = 81*36^(n-2) + 4^(n-2) - 18*12^(n-2).

G.f.: x*(1+12*x)/((1-4*x)*(1-12*x)*(1-36*x)). (End)

a(n) = A016129(n-1)^2. - Philippe Deléham, Nov 26 2008

a(n) = 4^(n-2) * (3^n - 1)^2. - Harvey P. Dale, Apr 15 2020

E.g.f.: (1/16)*exp(4*x)*(1 - 2*exp(8*x) + exp(32*x)). - G. C. Greubel, Oct 03 2024

Extensions

More terms from R. J. Mathar, Sep 24 2008