A117614 a(0)=1, a(n)=4a(n-1)+2 for n odd, a(n)=4a(n-1) for n even.

1, 6, 24, 98, 392, 1570, 6280, 25122, 100488, 401954, 1607816, 6431266, 25725064, 102900258, 411601032, 1646404130, 6585616520, 26342466082, 105369864328, 421479457314, 1685917829256, 6743671317026, 26974685268104

Offset

0,2

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).

Formula

a(n) = (-5-3*(-1)^n+23*4^n)/15. a(n) = 4*a(n-1)+a(n-2)-4*a(n-3). G.f.: -(x^2-2*x-1) / ((x-1)*(x+1)*(4*x-1)). [Colin Barker, Feb 17 2013]

Maple

a:=proc(n) if n=0 then 1 elif n mod 2 = 1 then 4*a(n-1)+2 else 4*a(n-1) fi end: seq(a(n), n=0..25);

Mathematica

b[0] := 1 b[1] := 6 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, 1}, 30][[All, 2]] (* or *) LinearRecurrence[{4, 1, -4}, {1, 6, 24}, 30] (* Harvey P. Dale, Nov 15 2020 *)

Crossrefs

Sequence in context: A290911 A037505 A048179 * A037688 A343116 A360036

Adjacent sequences: A117611 A117612 A117613 * A117615 A117616 A117617

Keyword

nonn,easy

Author

Roger L. Bagula, Apr 07 2006

Extensions

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

Status

approved