OFFSET
0,2
COMMENTS
1, 2, 4, 5, 7, 8, 1, 2, 4, 5, 7, 8, 1, 2, 4,...
1, 2, 1, 2, 1,-7, 1, 2, 1, 2, 1,-7, 1, 2, 1, 2,...
1,-1, 1, -1, -8, 8, 1,-1, 1, -1, -8, 8, 1, -1,..
-2, 2,-2, -7, 16,-7,-2, 2,-2, -7, 16,-7, -2,..
4,-4,-5, 23,-23, 5, 4,-4,-5, 23,-23, 5, 4,..
-8,-1,28,-46, 28,-1,-8,-1,28,-46, 28,-1,..
Reading downwards the main diagonal of this array defines the sequence.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (1,-1,3,6)
FORMULA
a(n) = ( -3*(-1)^n -2^n +3*(-1)^(floor((n-1)/2))*A108411(n) )/2, n>0. - R. J. Mathar, Mar 08 2011
a(4n)+a(4n+1)+a(4n+2)+a(4n+3) = -120*16^(n-1), n>0.
a(4n+2)+a(4n+3)+a(4n+4)+a(4n+5) = -30*A001025(n).
G.f. x*(-2+x+6*x^2+21*x^3) / ( (2*x-1)*(1+x)*(3*x^2+1) ). - R. J. Mathar, Mar 08 2011
MAPLE
A108411 := proc(n) 3^floor(n/2) ; end proc:
A141516 := proc(n) if n = 0 then 1; else (-3*(-1)^n-2^n+3*(-1)^(floor((n-1)/2))*A108411(n))/2 ; end if; end proc: # R. J. Mathar, Mar 08 2011
MATHEMATICA
LinearRecurrence[{1, -1, 3, 6}, {1, 2, 1, -7, -23}, 30] (* Harvey P. Dale, Nov 23 2022 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Aug 11 2008
STATUS
approved