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A003115
a(n) = 4^floor(n/2)*a(n-1) - a(n-2), for n >= 2, with a(0) = a(1) = 1.
(Formerly M2913)
2
1, 1, 3, 11, 173, 2757, 176275, 11278843, 2887207533, 739113849605, 756849694787987, 775013348349049083, 3174453917988010255981, 13002562473065541659449093, 213033980384251916560403683731
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
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
else: return 4^(n//2)*A003115(n-1) - A003115(n-2)
[A003115(n) for n in range(40)] # G. C. Greubel, Nov 04 2022
CROSSREFS
Sequence in context: A306002 A140538 A006485 * A053888 A118479 A103836
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Herman P. Robinson. Entry revised by N. J. A. Sloane, Jun 13 2012
EXTENSIONS
More terms from Michael Somos, Aug 23, 2000.
STATUS
approved