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 A082388 a(1) = 1, a(2) = 2; further terms are defined by rules that for k >= 2, a(2^k-i) = a(2^k+i) for 1 <= i <= 2^k-1 and a(2^k) = a(2^(k-1)) + Sum_{i < 2^k} a(i). 2
 1, 2, 1, 6, 1, 2, 1, 20, 1, 2, 1, 6, 1, 2, 1, 68, 1, 2, 1, 6, 1, 2, 1, 20, 1, 2, 1, 6, 1, 2, 1, 232, 1, 2, 1, 6, 1, 2, 1, 20, 1, 2, 1, 6, 1, 2, 1, 68, 1, 2, 1, 6, 1, 2, 1, 20, 1, 2, 1, 6, 1, 2, 1, 792, 1, 2, 1, 6, 1, 2, 1, 20, 1, 2, 1, 6, 1, 2, 1, 68, 1, 2, 1, 6, 1, 2, 1, 20, 1, 2, 1, 6, 1, 2, 1, 232, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1024 FORMULA a(2^k) = 4*a(2^(k-1)) - 2*a(2^(k-2)); a(2^k) = round((1/2)*(2+sqrt(2))^k). Multiplicative with a(2^e) = A006012(e), a(p^e) = 1 for odd prime p. - Andrew Howroyd, Jul 31 2018 MATHEMATICA a[n_] := With[{e = IntegerExponent[n, 2]}, Sum[Binomial[e, 2k] 2^(e-k), {k, 0, Quotient[e, 2]}]]; a /@ Range[1, 100] (* Jean-François Alcover, Sep 20 2019, from PARI *) PROG (PARI) a(n)={my(e=valuation(n, 2)); sum(k=0, e\2, binomial(e, 2*k)*2^(e-k))} \\ Andrew Howroyd, Jul 31 2018 CROSSREFS Cf. A006012. Sequence in context: A345461 A229818 A324500 * A178254 A085099 A193807 Adjacent sequences:  A082385 A082386 A082387 * A082389 A082390 A082391 KEYWORD nonn,mult AUTHOR Benoit Cloitre, Apr 14 2003 STATUS approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)