A164532 a(n) = 6*a(n-2) for n > 2; a(1) = 1, a(2) = 4.

1, 4, 6, 24, 36, 144, 216, 864, 1296, 5184, 7776, 31104, 46656, 186624, 279936, 1119744, 1679616, 6718464, 10077696, 40310784, 60466176, 241864704, 362797056, 1451188224, 2176782336, 8707129344, 13060694016, 52242776064, 78364164096

Offset

1,2

Comments

Interleaving of A000400 and A067411 without initial term 1.

Binomial transform is apparently A123011. Fourth binomial transform is A154235.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,6).

Formula

a(n) = (5 - (-1)^n)*6^(1/4*(2*n - 5 + (-1)^n)).

G.f.: x*(1+4*x)/(1-6*x^2).

a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011

a(n) = ((1-(-1)^n)*sqrt(6)/2 + 2*(1+(-1)^n))*6^(n/2 -1). - G. C. Greubel, Jul 16 2021

Mathematica

LinearRecurrence[{0, 6}, {1, 4}, 40] (* G. C. Greubel, Jul 16 2021 *)

Prog

(Magma) [ n le 2 select 3*n-2 else 6*Self(n-2): n in [1..29] ];
(Sage) [((1 - (-1)^n)*sqrt(6)/2 + 2*(1 + (-1)^n))*6^(n/2 -1) for n in (1..40)] # G. C. Greubel, Jul 16 2021

Crossrefs

Cf. A000400 (powers of 6), A067411, A123011, A154235.

Sequence in context: A174197 A071224 A305381 * A098660 A363631 A122174

Adjacent sequences: A164529 A164530 A164531 * A164533 A164534 A164535

Keyword

nonn

Author

Klaus Brockhaus, Aug 15 2009

Status

approved