A106706 a(0) = 19; for n>0, successively subtract 5, subtract 3 and double.

19, 14, 11, 22, 17, 14, 28, 23, 20, 40, 35, 32, 64, 59, 56, 112, 107, 104, 208, 203, 200, 400, 395, 392, 784, 779, 776, 1552, 1547, 1544, 3088, 3083, 3080, 6160, 6155, 6152, 12304, 12299, 12296, 24592, 24587, 24584, 49168, 49163, 49160, 98320, 98315, 98312, 196624

Offset

0,1

Comments

Suggested by a test found on the Internet.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Jeffrey N. Shaumeyer, Bearcastle Blog, One Post, Two ... [Via Internet Archive Wayback-Machine]

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-2).

Formula

G.f.: (19 + 14*x + 11*x^2 - 35*x^3 - 25*x^4 - 19*x^5)/((1 - 2*x^3)*(1 - x^3)).

a(3n) = 3*2^n+16, a(3n+1) = 3*2^n+11, a(3n+2) = 3*2^n+8.

Maple

f:=proc(n) option remember; if n=0 then RETURN(19); fi; if n mod 3 = 1 then RETURN(f(n-1)-5); elif n mod 3 = 2 then RETURN(f(n-1)-3); else RETURN(2*f(n-1)); fi; end;

Mathematica

nxt[{b_, c_, d_}]:={d-5, d-8, 2d-16}; Join[{19}, Flatten[NestList[nxt, {14, 11, 22}, 20]]] (* Harvey P. Dale, Dec 01 2019 *)

Prog

(PARI) a(n)=3*2^(n\3)+[16, 11, 8][n%3+1]  \\ M. F. Hasler, Nov 16 2010
(Magma) I:=[19, 14, 11, 22, 17, 14]; [n le 6 select I[n] else 3*Self(n-3) - 2*Self(n-6): n in [1..61]]; // G. C. Greubel, Sep 09 2021
(Sage)
def p(n): return 0 if (n%3==0) else 5 if (n%3==1) else 8
def a(n, b): return 2^(n//3)*(b-16) + 16 - p(n)
[a(n, 19) for n in (0..60)] # G. C. Greubel, Sep 09 2021

Crossrefs

Sequence in context: A177923 A155848 A088399 * A291427 A099939 A269231

Adjacent sequences: A106703 A106704 A106705 * A106707 A106708 A106709

Keyword

nonn

Author

N. J. A. Sloane, based on correspondence with Jeffrey N. Shaumeyer, Apr 23 2006

Status

approved