# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a098657 Showing 1-1 of 1 %I A098657 #13 Jul 14 2023 15:28:41 %S A098657 1,1,6,4,40,16,288,64,2176,256,16896,1024,133120,4096,1056768,16384, %T A098657 8421376,65536,67239936,262144,537395200,1048576,4297064448,4194304, %U A098657 34368126976,16777216,274911461376,67108864,2199157473280,268435456,17592722915328,1073741824 %N A098657 Expansion of (1-x-4x^2)/((1-2x)(1-8x^2)). %C A098657 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 A098657 P. Feinsilver and J. Kocik, Krawtchouk matrices from classical and quantum walks, Contemporary Mathematics, 287 2001, pp. 83-96. %H A098657 Index entries for linear recurrences with constant coefficients, signature (2,8,-16). %F A098657 a(n) = 2^((3*n-4)/2)*(1+(-1)^n)+2^(n-1). %F A098657 a(n) = 2*a(n-1) + 8*a(n-2) - 16*a(n-3). %F A098657 a(2n) = A081337(n) = (8^n+4^n)/2 and a(2n+1) = 4^n. - _Peter Kagey_, Jul 14 2023 %Y A098657 Cf. A081337, A098655, A098656. %K A098657 easy,nonn %O A098657 0,3 %A A098657 _Paul Barry_, Sep 19 2004 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE