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A176662

a(0)=2, a(1)=7, and a(n) = (3*n+1)*2^(n-1) if n > 1.

2, 7, 14, 40, 104, 256, 608, 1408, 3200, 7168, 15872, 34816, 75776, 163840, 352256, 753664, 1605632, 3407872, 7208960, 15204352, 31981568, 67108864, 140509184, 293601280, 612368384, 1275068416, 2650800128, 5502926848, 11408506880, 23622320128, 48855252992

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OFFSET

0,1

COMMENTS

The sequence appears on the main diagonal of the array defined by A123167 in the first row and successive differences in followup rows:

2, 3, 10, 7, 18, 11, 26, 15, 34, 19, ... A123167

1, 7, -3, 11, -7, 15, -11, 19, -15, 23, ... first diff

6, -10, 14, -18, 22 -26, 30, -34, 38, ... second diff

-16, 24, -32, 40, -48, 56, -64, 72, -80, ... third diff

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-4).

FORMULA

a(n) mod 9 = A010710(n-1), n > 2.

a(2n) + a(2n+1) = 9, 54, 360, 2016, ...

a(n) - 2*a(n-1) = 12*A131577(n-2), n > 1.

a(n) = 4*a(n-1) - 4*a(n-2), n > 3.

G.f.: (-6*x^2+12*x^3+2-x)/(1-2*x)^2.

MATHEMATICA

LinearRecurrence[{4, -4}, {2, 7, 14, 40}, 40] (* or *) Join[{2, 7}, Table[ (3n+1) 2^(n-1), {n, 2, 40}]] (* Harvey P. Dale, Oct 05 2019 *)

CROSSREFS

Sequence in context: A194590 A107373 A336579 * A018526 A329115 A018542

Adjacent sequences: A176659 A176660 A176661 * A176663 A176664 A176665

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Apr 23 2010

EXTENSIONS

Edited by R. J. Mathar, Jun 30 2010

STATUS

approved