A164346 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

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).

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

MATHEMATICA

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

PROG

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

(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

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.

Sequence in context: A254942 A077828 A002001 * A113956 A323261 A103943

Adjacent sequences: A164343 A164344 A164345 * A164347 A164348 A164349

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Aug 13 2009

STATUS

approved