OFFSET
0,3
REFERENCES
D. H. Lehmer, Course on History of Mathematics, Univ. Calif. Berkeley, 1973.
H. P. Robinson, Letter to N. J. A. Sloane, Oct 23 1973.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..80
Herman P. Robinson, Letter to N. J. A. Sloane, Oct 1973.
FORMULA
a(n) = (4^(n-1) - 5)*a(n-2) - 4*a(n-4).
MATHEMATICA
nxt[{n_, a_, b_}]:={n+1, b, b*4^Floor[(n+1)/2]-a}; NestList[nxt, {1, 1, 1}, 15][[All, 2]] (* Harvey P. Dale, Oct 12 2019 *)
PROG
(PARI) a(n)=if(n<2, n >= 0, 4^(n\2)*a(n-1)-a(n-2))
(Magma) I:=[1, 1, 3, 11]; [n le 4 select I[n] else (4^(n-2) -5)*Self(n-2) - 4*Self(n-4): n in [1..41]]; // G. C. Greubel, Nov 04 2022
(SageMath)
@CachedFunction
def A003115(n):
if (n<2): return 1
[A003115(n) for n in range(40)] # G. C. Greubel, Nov 04 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Michael Somos, Aug 23, 2000.
STATUS
approved