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A083233 a(n) = (3*8^n + 0^n)/4. 6
1, 6, 48, 384, 3072, 24576, 196608, 1572864, 12582912, 100663296, 805306368, 6442450944, 51539607552, 412316860416, 3298534883328, 26388279066624, 211106232532992, 1688849860263936, 13510798882111488, 108086391056891904, 864691128455135232 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A083232. Inverse binomial transform of A066443

Numbers n such that, except some first term, n^2 = [A000302]^3 + [A004171]^3 + [A002001]^3; e.g., 3072^2 = 64^3 + 128^3 + 192^3; 51539607552^2 = 4194304^3 + 8388608^3 + 12582912^3. - Vincenzo Librandi, Aug 08 2010

With the exception of the first term, these numbers cannot be written as the sum of two integer cubes but can be written as the sum of two positive rational cubes (i.e., 6*8^n = (17*2^n/21)^3 + (37*2^n/21)^3). - Arkadiusz Wesolowski, Aug 15 2013

LINKS

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (8).

FORMULA

a(n) = (3*8^n + 0^n)/4.

G.f.: (1-2x)/(1-8x).

E.g.f.: (3exp(8x) + exp(0))/4.

a(0) = 1, a(n+1) = 6*8^n. - Arkadiusz Wesolowski, Aug 15 2013

EXAMPLE

a(0) = (3*8^0 + 0^0)/4 = 4/4 = 1 (using 0^0 = 1).

PROG

(PARI) a(n)=(3*8^n+0^n)/4 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A083234. Subsequence of A159843.

Cf. A000302, A004171, A002001.

Sequence in context: A155130 A250164 A264083 * A002918 A005399 A258790

Adjacent sequences:  A083230 A083231 A083232 * A083234 A083235 A083236

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 23 2003

STATUS

approved

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Last modified May 26 21:59 EDT 2018. Contains 304646 sequences. (Running on oeis4.)