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%I #16 Sep 27 2023 16:42:12
%S 1,9,50,232,996,4124,16780,67692,271916,1089964,4364460,17467052,
%T 69886636,279583404,1118407340,4473776812,17895402156,71582198444,
%U 286329973420,1145322252972,4581293730476,18325184359084,73300756310700
%N a(n) = 6*a(n-1) - 8*a(n-2) + 4 for n > 1; a(0) = 1, a(1) = 9.
%C Inverse binomial transform of A016273.
%H Vincenzo Librandi, <a href="/A171480/b171480.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F a(n) = (25*4^n - 27*2^n + 8)/6.
%F G.f.: (1+x)^2/((1-x)*(1-2*x)*(1-4*x)).
%F E.g.f.: exp(x)*(8 - 27*exp(x) + 25*exp(3*x))/6. - _Stefano Spezia_, Sep 27 2023
%o (PARI) {m=23; v=concat([1, 9], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]+4); v}
%o (Magma) [(25*4^n-27*2^n+8)/6: n in [0..30]]; // _Vincenzo Librandi_, Jul 18 2011
%Y Cf. A016273 (expansion of 1/((1-2*x)*(1-3*x)*(1-5*x))), A171472, A171473.
%K nonn,easy
%O 0,2
%A _Klaus Brockhaus_, Dec 09 2009
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