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A164587
a(n) = 2*a(n - 2) for n > 2; a(1) = 1, a(2) = 8.
9
1, 8, 2, 16, 4, 32, 8, 64, 16, 128, 32, 256, 64, 512, 128, 1024, 256, 2048, 512, 4096, 1024, 8192, 2048, 16384, 4096, 32768, 8192, 65536, 16384, 131072, 32768, 262144, 65536, 524288, 131072, 1048576, 262144, 2097152, 524288, 4194304, 1048576
OFFSET
1,2
COMMENTS
Interleaving of A000079 and A000079 without initial terms 1, 2, 4.
Binomial transform is A048696. Second binomial transform is A164298.
FORMULA
a(n) = (5 + 3*(-1)^n)*2^((2*n -5 +(-1)^n)/4).
G.f.: x*(1+8*x)/(1-2*x^2).
E.g.f.: 4*cosh(sqrt(2)*x) + (1/sqrt(2))*sinh(sqrt(2)*x) - 4. - G. C. Greubel, Aug 12 2017
MATHEMATICA
CoefficientList[Series[(1 - x)/(1 - 10*x + 17*x^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 12 2017 *)
PROG
(Magma) [ n le 2 select 7*n-6 else 2*Self(n-2): n in [1..41] ];
(PARI) x='x+O('x^50); Vec(x*(1+8*x)/(1-2*x^2)) \\ G. C. Greubel, Aug 12 2017
CROSSREFS
Equals A112032 without initial term 4.
Cf. A000079 (powers of 2), A048696, A164298.
Sequence in context: A167623 A040063 A196170 * A050096 A161593 A008866
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Aug 17 2009
STATUS
approved