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

Author

Klaus Brockhaus, Aug 15 2009

Keywords

• nonn

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).

Crossrefs

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

Programs

Magma

[ n le 2 select 3*n-2 else 6*Self(n-2): n in [1..29] ];

Mathematica

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

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

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