cp's OEIS Frontend

A138414 A bisection of A000957.

%I A138414 #12 Apr 26 2023 18:31:45
%S A138414 1,1,6,57,622,7338,91144,1174281,15548694,210295326,2892818244,
%T A138414 40347919626,569274150156,8110508473252,116518215264492,
%U A138414 1686062250699433,24552388991392230,359526085719652662,5290709340633314596,78201907647506243758,1160507655117628665252,17283862221822154612428,258257655550682547281952
%N A138414 A bisection of A000957.
%F A138414 a(n) = A000957(2*n+1).
%p A138414 b:= proc(n) option remember; `if`(n<3, n*(2-n),
%p A138414       ((7*n-12)*b(n-1)+(4*n-6)*b(n-2))/(2*n))
%p A138414     end:
%p A138414 a:= n-> b(2*n+1):
%p A138414 seq(a(n), n=0..25);  # _Alois P. Heinz_, Apr 26 2023
%o A138414 (PARI)
%o A138414 x='x+O('x^100);  v=Vec((1-sqrt(1-4*x))/(3-sqrt(1-4*x)));
%o A138414 vector(#v\2,n,v[2*n-1]) /* show terms */
%o A138414 (Python)
%o A138414 from itertools import count, islice
%o A138414 def A138414_gen(): # generator of terms
%o A138414     yield 1
%o A138414     a, c = 0, 1
%o A138414     for n in count(1,2):
%o A138414         yield (a:=(c:=c*((n<<2)+2)//(n+2))-a>>1)
%o A138414         a=(c:=c*((n+1<<2)+2)//(n+3))-a>>1
%o A138414 A138414_list = list(islice(A138414_gen(),20)) # _Chai Wah Wu_, Apr 26 2023
%Y A138414 Cf. A000957, A138413.
%K A138414 nonn,easy
%O A138414 0,3
%A A138414 _N. J. A. Sloane_, May 08 2008