OFFSET
0,2
REFERENCES
M. Gardner, Riddles of the Sphinx, New Mathematical Library, M.A.A., 1987, p. 145. Math. Rev. 89i:00015.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,8).
FORMULA
G.f.: 3*x/((1+2*x)*(1-4*x)).
a(n) = 3*A003683(n).
Given the 2 X 2 matrix M = [1,3; 3,1], a(n) = term (1,2) in M^n, n>0. - Gary W. Adamson, Aug 06 2010
From G. C. Greubel, Feb 17 2023: (Start)
a(n) = 2*a(n-1) + 8*a(n-2).
a(n) = 3*2^(n-1)*A001045(n).
a(n) = 2^(n-1)*A062510(n).
a(n) = (1/2)*A071930(n+1).
E.g.f.: (1/2)*(exp(4*x) - exp(-2*x)). (End)
MATHEMATICA
Table[(4^n-(-2)^n)/2, {n, 0, 40}] (* G. C. Greubel, Feb 17 2023 *)
PROG
(PARI) a(n)=if(n<0, 0, 2^(n-1)*(2^n-(-1)^n))
(Magma) [(4^n -(-2)^n)/2: n in [0..40]]; // G. C. Greubel, Feb 17 2023
(SageMath) [(4^n-(-2)^n)/2 for n in range(41)] # G. C. Greubel, Feb 17 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved