%I #13 Jul 14 2023 15:28:41

%S 1,1,6,4,40,16,288,64,2176,256,16896,1024,133120,4096,1056768,16384,

%T 8421376,65536,67239936,262144,537395200,1048576,4297064448,4194304,

%U 34368126976,16777216,274911461376,67108864,2199157473280,268435456,17592722915328,1073741824

%N Expansion of (1-x-4x^2)/((1-2x)(1-8x^2)).

%C Let A=[1,2,1;2,0,-2;1,-2,1] the 3 X 3 symmetric Krawtchouk matrix. Then a(n) is the 1,1 element of A^n.

%D P. Feinsilver and J. Kocik, Krawtchouk matrices from classical and quantum walks, Contemporary Mathematics, 287 2001, pp. 83-96.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,8,-16).

%F a(n) = 2^((3*n-4)/2)*(1+(-1)^n)+2^(n-1).

%F a(n) = 2*a(n-1) + 8*a(n-2) - 16*a(n-3).

%F a(2n) = A081337(n) = (8^n+4^n)/2 and a(2n+1) = 4^n. - _Peter Kagey_, Jul 14 2023

%Y Cf. A081337, A098655, A098656.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Sep 19 2004