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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Interleaving of A000079 and A000079 without initial terms 1, 2, 4. Binomial transform is A048696. Second binomial transform is A164298. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 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 Adjacent sequences:  A164584 A164585 A164586 * A164588 A164589 A164590 KEYWORD nonn AUTHOR Klaus Brockhaus, Aug 17 2009 STATUS approved

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