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

0,2

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).

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

Mathematica

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

Prog

(Magma) [ (3*2^n-2)*2^n: n in [0..23] ];
(PARI) a(n)=(3*2^n-2)*2^n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

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

Sequence in context: A217375 A113071 A006726 * A000760 A171189 A272050

Adjacent sequences: A165662 A165663 A165664 * A165666 A165667 A165668

Keyword

nonn,easy

Author

Klaus Brockhaus, Sep 24 2009

Status

approved