A218009 Binomial transform of A212831(n).
0, 1, 4, 12, 30, 70, 160, 364, 824, 1848, 4096, 8976, 19488, 42016, 90112, 192448, 409472, 868224, 1835008, 3866880, 8126976, 17039872, 35651584, 74447872, 155187200, 322959360, 671088640, 1392513024, 2885689344, 5972697088, 12348030976, 25501351936, 52613316608
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-8).
Programs
-
Magma
I:=[0, 1, 4, 12, 30, 70]; [n le 6 select I[n] else 6*Self(n-1) - 14*Self(n-2) + 16*Self(n-3) - 8*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 15 2012
-
Mathematica
a[n_] := Sum[(1/4)*Binomial[n, k]*((-(1 + (-1)^k))*(-1 + (-1)^Floor[k/2]) - (-3 + (-1)^k)*k), {k, 0, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Oct 18 2012 *) CoefficientList[Series[x*(1 - 2*x + 2*x^2 - 2*x^3 + 2*x^4)/((1 - 2*x)^2*(1 - 2*x + 2*x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 15 2012 *)
Formula
G.f.: x*(1-2*x+2*x^2-2*x^3+2*x^4)/((1-2*x)^2*(1-2*x+2*x^2)). - Bruno Berselli, Oct 18 2012
a(n) = 2^(n-3)*(3*n+2)+(1+i)^(n-4)+(1-i)^(n-4), where i=sqrt(-1) and n>1, with a(0)=0, a(1)=1. - Bruno Berselli, Oct 18 2012
a(n) = 6*a(n-1) -14*a(n-2) +16*a(n-3) -8*a(n-4).
Comments