cp's OEIS Frontend

A099252 Bisection of A005043.

%I A099252 #30 Jul 26 2020 04:20:40
%S A099252 0,1,6,36,232,1585,11298,83097,625992,4805595,37458330,295673994,
%T A099252 2358641376,18985057351,154000562758,1257643249140,10331450919456,
%U A099252 85317692667643,707854577312178,5897493615536452,49320944483427000,413887836110423787,3484084625456932134,29412628894558563849
%N A099252 Bisection of A005043.
%D A099252 G. F. Smith, On isotropic tensors and rotation tensors of dimension m and order n, Tensor (N.S.), Vol. 19 (1968), 79-88 (MR0224008).
%H A099252 Vincenzo Librandi, <a href="/A099252/b099252.txt">Table of n, a(n) for n = 0..200</a>
%H A099252 D. L. Andrews, <a href="/A005043/a005043.pdf">Letter to N. J. A. Sloane</a>, Apr 10 1978.
%F A099252 Recurrence: (n+1)*(2*n+1)*a(n) = n*(26*n-7)*a(n-1) - 3*(26*n^2 - 61*n + 39)*a(n-2) + 27*(n-2)*(2*n-3)*a(n-3). - _Vaclav Kotesovec_, Oct 17 2012
%F A099252 a(n) ~ 3^(2*n+5/2)/(16*sqrt(2*Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 17 2012
%F A099252 a(n) = -hypergeom([-2*n - 1, 1/2], [2], 4). - _Peter Luschny_, Jul 26 2020
%p A099252 G := (1+x-sqrt(1-2*x-3*x^2))/(2*x*(1+x)): Gser := series(G,x=0,60):
%p A099252 seq(coeff(Gser, x^(2*n-1)), n=1..25); # _Emeric Deutsch_
%p A099252 a := n -> -hypergeom([-2*n-1, 1/2], [2], 4):
%p A099252 seq(simplify(a(n)), n=0..23); # _Peter Luschny_, Jul 26 2020
%t A099252 Take[CoefficientList[Series[(1+x-Sqrt[1-2*x-3*x^2])/(2*x*(1+x)), {x, 0, 60}], x], {2, -1, 2}] (* _Vaclav Kotesovec_, Oct 17 2012 *)
%o A099252 (PARI) x='x+O('x^66); v=Vec((1+x-sqrt(1-2*x-3*x^2))/(2*x*(1+x))); vector(#v\2,n,v[2*n]) \\ _Joerg Arndt_, May 12 2013
%o A099252 (Sage)
%o A099252 def A():
%o A099252     a, b, c, d, n = 0, 1, 1, -1, 1
%o A099252     yield 0
%o A099252     while True:
%o A099252         n += 1
%o A099252         a, b = b, (3*(n-1)*n*a+(2*n-1)*n*b)//((n+1)*(n-1))
%o A099252         c, d = d, (3*(n-1)*c-(2*n-1)*d)//n
%o A099252         if n%2: yield -(d + b)*(1-(-1)^n)//2
%o A099252 A099252  = A()
%o A099252 print([next(A099252) for _ in range(24)]) # _Peter Luschny_, May 16 2016
%Y A099252 Cf. A005043, A099251.
%K A099252 nonn,easy
%O A099252 0,3
%A A099252 _N. J. A. Sloane_, Nov 16 2004
%E A099252 More terms from _Emeric Deutsch_, Nov 18 2004