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A120743 a(n) = (1/2)*(1+3*I)^n + (1/2)*(1-3*I)^n. 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

Comment from R. J. Mathar, Jun 15 2007: 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=1..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;

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

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

CROSSREFS

Cf. A006495

Sequence in context: A060743 A029617 A200785 * A063560 A265104 A271989

Adjacent sequences:  A120740 A120741 A120742 * A120744 A120745 A120746

KEYWORD

easy,sign

AUTHOR

Creighton Dement, Jun 11 2007

EXTENSIONS

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

STATUS

approved

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Last modified November 17 19:58 EST 2017. Contains 294834 sequences.