OFFSET
0,2
COMMENTS
a(n) and successive differences define an infinite array:
1, 2, 4, 2, 4, 8, ...
1, 2, -2, 2, 4, 14, ...
1, -4, 4, 2, 10, 8, ...
-5, 8, -2, 8, -2, 14, ...
13, -10, 10, -10, 16, 2, ...
-23, 20, -20, 26, -14, 32, ...
...
Its main diagonal consists of the powers 2^n. The first upper diagonal is a signed sequence of 2's. The second upper diagonal contains essentially A135440.
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).
FORMULA
a(n+3) = 3*2^n - a(n), n >= 0.
a(n+1) - 2*a(n) = -6*A131531(n+1).
a(n+6) = a(n) + 21*2^n.
a(n) = ((2^n + 2*(-1)^n)*2^n - 2*i*sqrt(3)*((1+i*sqrt(3))^n - (1-i*sqrt(3))^n))/(3*2^n), where i=sqrt(-1); a(n+1) = 2*(A001045(n) + A010892(n)). - Bruno Berselli, Jun 06 2011
G.f.: ( -1+5*x^3 ) / ( (2*x-1)*(1+x)*(x^2-x+1) ). - R. J. Mathar, Jun 06 2011
a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4). - Paul Curtz, Jun 07 2011
MAPLE
A010892 := proc(n) op( 1+(n mod 6), [1, 1, 0, -1, -1, 0]) ; end proc:
seq(A191370(n), n=0..30) ; # R. J. Mathar, Jun 06 2011
MATHEMATICA
LinearRecurrence[{2, 0, -1, 2}, {1, 2, 4, 2}, 30] (* Harvey P. Dale, Sep 06 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jun 01 2011
STATUS
approved