

A128415


Expansion of (14x^2)/(1+3x+4x^2).


3



1, 3, 1, 9, 31, 57, 47, 87, 449, 999, 1201, 393, 5983, 16377, 25199, 10089, 70529, 251943, 473713, 413367, 654751, 3617721, 8234159, 10231593, 2241857, 47651943, 133988401, 211357431, 98118689
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Row sums of number triangle A128414.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,4).


FORMULA

For n>0, a(n) = (1/r)^n + (1/s)^n, with r = (3i*sqrt(7))/8 and s = (3+i*sqrt(7))/8 the roots of 4x^2+3x+1.  Ralf Stephan, Jul 20 2013
a(n) = 3*a(n1)  4*a(n2) for n > 2.  Harry Richman, May 05 2020


MATHEMATICA

CoefficientList[Series[(1  4 x^2) / (1 + 3 x + 4 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 20 2013 *)


CROSSREFS

Sequence in context: A273464 A105951 A038202 * A227795 A090479 A227758
Adjacent sequences: A128412 A128413 A128414 * A128416 A128417 A128418


KEYWORD

easy,sign


AUTHOR

Paul Barry, Mar 02 2007


STATUS

approved



