Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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