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A019464 Multiply by 1, add 1, multiply by 2, add 2, etc., start with 1.

%I A019464 #34 Aug 04 2025 11:08:53
%S A019464 1,1,2,4,6,18,21,84,88,440,445,2670,2676,18732,18739,149912,149920,
%T A019464 1349280,1349289,13492890,13492900,148421900,148421911,1781062932,
%U A019464 1781062944,23153818272,23153818285,324153455990,324153456004,4862301840060,4862301840075,77796829441200
%N A019464 Multiply by 1, add 1, multiply by 2, add 2, etc., start with 1.
%H A019464 Reinhard Zumkeller, <a href="/A019464/b019464.txt">Table of n, a(n) for n = 0..500</a>
%F A019464 For n>=1, a(2n)=floor((1+e)*(n-1)!)-1, a(2n+1)=floor((1+e)*(n+1)!)-n-2. - _Benoit Cloitre_, Apr 29 2003
%F A019464 a(n+1) = (1/2)*a(n)*(n+1 mod 2)*(n+2) + (1/2)*(n mod 2)*(2*a(n)+n+1). - Francois Jooste (pin(AT)myway.com), Jun 25 2003
%F A019464 a(n) = (n mod 2)*(floor((1+e)*(floor(n/2)+1)!)-floor(n/2)-2)+((n+1) mod 2)*(floor((1+e)*floor(n/2)!)-1) for n >= 1 with a(0) = 1. - _Wesley Ivan Hurt_, Aug 04 2025
%t A019464 a[n_?EvenQ] := n/2 + a[n-1]; a[n_?OddQ] := (n+1)*a[n-1]/2;
%t A019464 a[0] = 1; Table[a[n], {n, 0, 27}] (* _Jean-François Alcover_, Nov 15 2011 *)
%o A019464 (Haskell)
%o A019464 a019464 n = a019464_list !! n
%o A019464 a019464_list = 1 : concat (unfoldr ma (1, [1, 1])) where
%o A019464    ma (x, [_, j]) = Just (ij', (x + 1, ij')) where ij' = [x * j, x * j + x]
%o A019464 -- _Reinhard Zumkeller_, Nov 14 2011
%o A019464 (PARI) A019464(n,a=1)={for(i=2,n+1,if(bittest(i,0),a+=i\2,a*=i\2));a} \\ _M. F. Hasler_, Feb 25 2018
%Y A019464 Cf. A033540 (=a(2n)).
%Y A019464 Cf. A082458 (same, but start with 0), A019465 (start with 2), A019466 (start with 3).
%Y A019464 Cf. A019460 .. A019463 & A082448 (similar, but first add, then multiply).
%K A019464 nonn,easy,nice
%O A019464 0,3
%A A019464 _N. J. A. Sloane_
%E A019464 Edited by _M. F. Hasler_, Feb 25 2018