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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
FORMULA
a(n) = 2*a(n-1) - 10*a(n-2).
G.f.: x*(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
a(n) = A190958(n)-10*A190958(n-1). - R. J. Mathar, Dec 13 2022
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
Sequence in context: A060743 A029617 A200785 * A345205 A063560 A265104
KEYWORD
easy,sign
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 February 25 07:35 EST 2024. Contains 370310 sequences. (Running on oeis4.)