A164346 a(n) = 3 * 4^n.

3, 12, 48, 192, 768, 3072, 12288, 49152, 196608, 786432, 3145728, 12582912, 50331648, 201326592, 805306368, 3221225472, 12884901888, 51539607552, 206158430208, 824633720832, 3298534883328, 13194139533312, 52776558133248, 211106232532992, 844424930131968

Offset: 0

Author

Klaus Brockhaus, Aug 13 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A000244 without initial 1.

Second binomial transform of A007283.

Third binomial transform of A010701.

Inverse binomial transform of A005053 without initial 1.

First differences of A024036. - Omar E. Pol, Feb 16 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (4).

Crossrefs

Cf. A000302 (powers of 4), A000244 (powers of 3), A007283 (3*2^n), A010701 (all 3's), A005053, A002001, A096045, A140660 (3*4^n+1), A002023 (6*4^n), A002063(9*4^n), A056120, A084509.

Programs

Magma

[ 3*4^n: n in [0..22] ];

Mathematica

3 4^Range[0,30]  (* Harvey P. Dale, Mar 11 2011 *)

PARI

A164346(n)=3*4^n \\ M. F. Hasler, Jul 28 2015

Python

def A164346(n): return 3<<(n<<1) # Chai Wah Wu, Aug 30 2024

Formula

a(n) = 4*a(n-1) for n > 1; a(0) = 3.

G.f.: 3/(1-4*x).

a(n) = A002001(n+1). a(n) = A096045(n)+2. a(n) = A140660(n)-1.

a(n) = A002023(n)/2. a(n) = A002063(n)/3. a(n) = A056120(n+3)/9.

Apparently a(n) = A084509(n+3)/2.

a(n) = A110594(n+1), n>1. - R. J. Mathar, Aug 17 2009

a(n) = 3*A000302(n). - Omar E. Pol, Feb 18 2013

a(n) = A000079(2*n) + A000079(2*n+1). - M. F. Hasler, Jul 28 2015

E.g.f.: 3*exp(4*x). - G. C. Greubel, Sep 15 2017