A228305 a(1) = 3; for n >= 1, a(2*n) = 2^(n+1), a(2*n+1) = 5*2^(n-1).
3, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048, 2560, 4096, 5120, 8192, 10240, 16384, 20480, 32768, 40960, 65536, 81920, 131072, 163840, 262144, 327680, 524288, 655360, 1048576, 1310720, 2097152, 2621440, 4194304, 5242880
Offset: 1
Examples
a(9) = 40 because it is equal to 5*2^(4-1).
Links
- Wikipedia, Cube (algebra)
- Index entries for linear recurrences with constant coefficients, signature (0,2).
Programs
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Magma
[n le 3 select n+2 else 2*Self(n-2) : n in [1..43]];
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Mathematica
CoefficientList[Series[(3 + 4 x - x^2)/(1 - 2 x^2), {x, 0, 50}], x] (* Bruno Berselli, Aug 20 2013 *) -
PARI
r=43; print1(3); print1(", "); for(n=2, r, if(bitand(n, 1), print1(5*2^((n-3)/2)), print1(2^(n/2+1))); print1(", "));
Formula
a(n) = ceiling((9 - (- 1)^n)*2^(floor(n/2) - 2)).
a(n) = n + 2 for n <= 3; a(n) = 2*a(n-2) for n > 3.
From Bruno Berselli, Aug 20 2013: (Start)
G.f.: x*(3+4*x-x^2)/(1-2*x^2).
a(n) = (16-(8-5*r)*(1-(-1)^n))*r^(n-6) for n>1, r=sqrt(2). (End)
E.g.f.: (8*cosh(sqrt(2)*x) + 5*sqrt(2)*sinh(sqrt(2)*x) + 2*x - 8)/4. - Stefano Spezia, Apr 09 2025
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