|
|
A061084
|
|
Fibonacci-type sequence based on subtraction: a(0) = 1, a(1) = 2 and a(n) = a(n-2)-a(n-1).
|
|
22
|
|
|
1, 2, -1, 3, -4, 7, -11, 18, -29, 47, -76, 123, -199, 322, -521, 843, -1364, 2207, -3571, 5778, -9349, 15127, -24476, 39603, -64079, 103682, -167761, 271443, -439204, 710647, -1149851, 1860498, -3010349, 4870847, -7881196, 12752043, -20633239, 33385282, -54018521
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
If we drop 1 and start with 2 this is the Lucas sequence V(-1,-1). G.f.: (2+x)/(1+x-x^2). In this case a(n) is also the trace of A^(-n), where A is the Fibomatrix ((1,1), (1,0)). - Mario Catalani (mario.catalani(AT)unito.it), Aug 17 2002
The positive sequence with g.f. (1+x-2x^2)/(1-x-x^2) gives the diagonal sums of the Riordan array (1+2x,x/(1-x)). - Paul Barry, Jul 18 2005
Pisano period lengths: 1, 3, 8, 6, 4, 24, 16, 12, 24, 12, 10, 24, 28, 48, 8, 24, 36, 24, 18, 12, .... (is this A106291?). - R. J. Mathar, Aug 10 2012
|
|
LINKS
|
|
|
FORMULA
|
O.g.f.: (3*x+1)/(1+x-x^2). - Len Smiley, Dec 02 2001
|
|
EXAMPLE
|
a(6) = a(4)-a(5) = -4 - 7 = -11.
|
|
MATHEMATICA
|
LinearRecurrence[{-1, 1}, {1, 2}, 40] (* Harvey P. Dale, Nov 22 2011 *)
|
|
PROG
|
(Haskell)
a061084 n = a061084_list !! n
a061084_list = 1 : 2 : zipWith (-) a061084_list (tail a061084_list)
|
|
CROSSREFS
|
Cf. A061083 for division, A000301 for multiplication and A000045 for addition - the common Fibonacci numbers.
|
|
KEYWORD
|
sign,easy,nice
|
|
AUTHOR
|
Ulrich Schimke (ulrschimke(AT)aol.com)
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|