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A120743 a(n) = (1/2)*(1 + 3*i)^n + (1/2)*(1 - 3*i)^n where i = sqrt(-1). 3
1, -8, -26, 28, 316, 352, -2456, -8432, 7696, 99712, 122464, -752192, -2729024, 2063872, 31417984, 42197248, -229785344, -881543168, 534767104, 9884965888, 14422260736, -70005137408, -284232882176, 131585609728, 3105500041216 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From R. J. Mathar, Jun 15 2007: (Start)

These are the row sums of the triangle A013610 after every 2nd column is deleted, then every 2nd column reversed in sign, creating an intermediate irregular triangle with entries C(n,2*k)*(-9)^k, k = 0..floor(n/2):

  1;

  1,   -9;

  1,  -27;

  1,  -54,    81;

  1,  -90,   405;

  1, -135,  1215,    -729;

  1, -189,  2835,   -5103;

  1, -252,  5670,  -20412,   6561;

  1, -324, 10206,  -61236,  59049;

  1, -405, 17010, -153090, 295245, -59049; (End)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

Index entries for linear recurrences with constant coefficients, signature (2, -10).

FORMULA

a(n) = 2*a(n-1) - 10*a(n-2).

G.f.: (1-10*x)/(10*x^2 - 2*x + 1).

a(n) mod 9 = 1. - Paul Curtz, Apr 20 2011

G.f.: G(0)/(2*x) - 1/x, where G(k) = 1 + 1/(1 - x*(9*k+1)/(x*(9*k+10) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 29 2013

E.g.f.: exp(x)*cos(3*x). - Sergei N. Gladkovskii, May 29 2013

MATHEMATICA

LinearRecurrence[{2, -10}, {1, -8}, 30] (* G. C. Greubel, Nov 09 2018 *)

PROG

Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[A*B] with A = + 1.5i' + .5j' + .5k' + .5e and B = 'ji' + e

(MAGMA) [ n eq 1 select 1 else n eq 2 select -8 else 2*Self(n-1) -10*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 24 2011

(PARI) x='x+O('x^30); Vec((1-10*x)/(1-2*x+10*x^2)) \\ G. C. Greubel, Nov 09 2018

CROSSREFS

Cf. A006495

Sequence in context: A060743 A029617 A200785 * A063560 A265104 A304910

Adjacent sequences:  A120740 A120741 A120742 * A120744 A120745 A120746

KEYWORD

easy,sign,changed

AUTHOR

Creighton Dement, Jun 11 2007

EXTENSIONS

a(0)=1: a(n) is main diagonal of A009116(n). - Paul Curtz, Jul 22 2011

Edited by Jon E. Schoenfield, Nov 09 2018

STATUS

approved

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Last modified November 13 17:16 EST 2018. Contains 317149 sequences. (Running on oeis4.)