OFFSET
0,4
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..3036
Milica Anđelić and Carlos M. da Fonseca, On the constant coefficients of a certain recurrence relation: A simple proof, Heliyon (2021) Vol. 7, No. 8, e07764.
Sean A. Irvine, Walks on Graphs.
D. Panario, M. Sahin and Q. Wang, A family of Fibonacci-like conditional sequences, INTEGERS, Vol. 13, 2013, #A78.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Jeffrey Shallit, On the worst case of three algorithms for computing the Jacobi symbol, J. Symbolic Comput. 10 (1990), no. 6, 593-610.
Index entries for linear recurrences with constant coefficients, signature (0,5,0,-2).
FORMULA
Also a(n) = a(n-1) + 2a(n-2) if n is even, else a(n) = 2a(n-1) + a(n-2).
g.f.: -x*(2*x+1)*(x-1)/(1-5*x^2+2*x^4). Simon Plouffe in his 1992 dissertation.
a(2n+1) = A052984(n). [Index corrected by R. J. Mathar, Apr 01 2009]
a(2n) = A107839(n-1). [R. J. Mathar, Apr 01 2009]
MATHEMATICA
a[0] = 0; a[1] = 1; a[n_] := a[n] = If[ EvenQ[n], a[n - 1] + 2a[n - 2], 2a[n - 1] + a[n - 2]]; Table[a[n], {n, 0, 31}]
LinearRecurrence[{0, 5, 0, -2}, {0, 1, 1, 3}, 40] (* Harvey P. Dale, Jul 09 2015 *)
PROG
(PARI) A005824(n)=([5, -2; 1, 0]^(n\2)*if(n%2, [3, 1], [1, 0])~)[2]; \\ M. F. Hasler, Jan 13 2026
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Extended by Robert G. Wilson v, Dec 29 2002
STATUS
approved