A003115 a(n) = 4^floor(n/2)*a(n-1) - a(n-2), for n >= 2, with a(0) = a(1) = 1. (Formerly M2913)

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

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
    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

Adjacent sequences: A003112 A003113 A003114 * A003116 A003117 A003118

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