A165665 a(n) = (3*2^n - 2) * 2^n.

1, 8, 40, 176, 736, 3008, 12160, 48896, 196096, 785408, 3143680, 12578816, 50323456, 201310208, 805273600, 3221159936, 12884770816, 51539345408, 206157905920, 824632672256, 3298532786176, 13194135339008, 52776549744640

Offset: 0

Author

Klaus Brockhaus, Sep 24 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A058481. Second binomial transform of (A082505 without initial term 0). Third binomial transform of A010686.

Partial sums are in A060867.

a(n) is the sum of the odd numbers taken progressively by moving through them by 2^n-tuples. a(0)=1; a(1) = 3+5=8; a(2) = 7+9+11+13 = 40; a(3) = 15+17+19+21+23+25+27+29 = 176; a(n) = sum_{k=0,1,..,A000225(n)} (A000225(n+1)+2*k). - J. M. Bergot, Dec 06 2014

The number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 773", based on the 5-celled von Neumann neighborhood. - Robert Price, May 23 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (6,-8).

Crossrefs

Cf. A058481, A082505, A010686 (repeat 1, 5), A060867, A010036, A124647.

Programs

Magma

[ (3*2^n-2)*2^n: n in [0..23] ];

Mathematica

Table[(3*2^n-2)2^n,{n,0,30}] (* or  *) LinearRecurrence[{6,-8},{1,8},30] (* Harvey P. Dale, Nov 18 2020 *)

PARI

a(n)=(3*2^n-2)*2^n \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 6*a(n-1)-8*a(n-2) for n > 1; a(0) = 1, a(1) = 8.

a(n) = 8*A010036(n-1) for n > 0.

G.f.: (2*x+1)/((1-2*x)*(1-4*x)).

E.g.f.: 3*e^(4*x) - 2*e^(2*x). - Robert Israel, Dec 15 2014