A117615 a(0)=0, a(1)=1, a(n)=4a(n-1)+2 for n =3,5,7,..., a(n)=4a(n-1) for n =2,4,6,....

0, 1, 4, 18, 72, 290, 1160, 4642, 18568, 74274, 297096, 1188386, 4753544, 19014178, 76056712, 304226850, 1216907400, 4867629602, 19470518408, 77882073634, 311528294536, 1246113178146, 4984452712584, 19937810850338, 79751243401352

Offset

0,3

References

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

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (4, 1, -4).

Formula

G.f.: x*(1+x^2) / ( (x-1)*(4*x-1)*(1+x) ). - R. J. Mathar, Nov 07 2015

a(n) = 3*a(n-1)+4*a(n-2)+2,n>=3. - R. J. Mathar, Nov 07 2015

Maple

a:=proc(n) if n=0 then 0 elif n=1 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..24);

Mathematica

b[0] := 0 b[1] := 1 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]}; Join[{0}, Transpose[NestList[nxt, {1, 1}, 30]][[2]]] (* or *) Join[{0}, LinearRecurrence[{4, 1, -4}, {1, 4, 18}, 30]] (* Harvey P. Dale, Nov 28 2013 *)

Crossrefs

Sequence in context: A290919 A218892 A307566 * A267450 A199524 A083693

Adjacent sequences: A117612 A117613 A117614 * A117616 A117617 A117618

Keyword

nonn,easy

Author

Roger L. Bagula, Apr 07 2006

Extensions

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

Status

approved