A003073 A nonlinear recurrence. (Formerly M0282)

1, 1, 2, 2, 3, 4, 5, 7, 9, 11, 14, 18, 23, 29, 38, 47, 59, 76, 95, 120, 154, 191, 241, 310, 383, 483, 620, 767, 968, 1242, 1535, 1937, 2486, 3071, 3875, 4972, 6143, 7752, 9946, 12287, 15505, 19894, 24575, 31011, 39788, 49151, 62024, 79578, 98303

Offset

0,3

References

D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, p. 208.

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..5000

Mathematica

A003073[n_]:= If[Mod[n, 3]==0, Floor[3*2^Floor[n/3]/2] - Boole[Floor[n/3] >0], If[Mod[n, 3]==2, 2*Floor[17*2^Floor[n/3]/14] +Boole[Floor[n/3] == 2], Floor[53*2^Floor[n/3]/28] - Boole[Floor[n/3] >2] ]];
Table[A003073[n], {n, 0, 60}] (* G. C. Greubel, Nov 03 2022 *)

Prog

(PARI) a(n)=local(k); k=n\3; if(n%3==0, 3*2^k\2-(k>0), if(n%3==2, 2*(17*2^k\14)+(k==2), 53*2^k\28-(k>2))) /* Michael Somos, May 04 2000 */
(SageMath)
def A003073(n):
    if (n%3==0): return ((3*2^(n//3))//2) - int((n//3)>0)
    elif (n%3==2): return 2*((17*2^(n//3))//14) + int((n//3)==2)
    else: return ((53*2^(n//3))//28) - int((n//3)>2)
[A003073(n) for n in range(61)] # G. C. Greubel, Nov 03 2022

Crossrefs

Sequence in context: A280663 A052816 A122130 * A123946 A002569 A129528

Adjacent sequences: A003070 A003071 A003072 * A003074 A003075 A003076

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Michael Somos, May 04 2000

Status

approved