A117616 a(0)=0, a(n)=4a(n-1)+2 for n odd, a(n)=4a(n-1) for n even.

0, 2, 8, 34, 136, 546, 2184, 8738, 34952, 139810, 559240, 2236962, 8947848, 35791394, 143165576, 572662306, 2290649224, 9162596898, 36650387592, 146601550370, 586406201480, 2345624805922, 9382499223688, 37529996894754

Offset: 0

Author

Roger L. Bagula, Apr 07 2006

Keywords

• nonn
• easy

References

• L. Rosenfeld, Nuclear Forces, section II, Interscience, New York, 1948, p 202

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,1,-4).

Programs

Maple

a:=proc(n) if n=0 then 0 elif n mod 2 = 1 then 4*a(n-1)+2 else 4*a(n-1) fi end: seq(a(n),n=0..23);

Mathematica

b[0] := 0 b[1] := 2 b[n_?EvenQ] := b[n] = 4*b[n - 1] b[n_?OddQ] := b[n] = 4*b[n - 1] + 2 a = Table[b[n], {n, 0, 25}]
nxt[{n_,a_}]:={n+1,If[EvenQ[n],4a+2,4a]}; NestList[nxt,{0,0},30][[;;,2]] (* or *) LinearRecurrence[{4,1,-4},{0,2,8},30] (* Harvey P. Dale, Mar 10 2023 *)

Formula

a(n) = (-5-3*(-1)^n+2^(3+2*n))/15. a(n) = 4*a(n-1)+a(n-2)-4*a(n-3). G.f.: 2*x / ((x-1)*(x+1)*(4*x-1)). [Colin Barker, Feb 17 2013]

a(n) = 2*A033114(n). - R. J. Mathar, Feb 27 2019

Extensions

Edited by N. J. A. Sloane, Apr 16 2006