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%I #21 Nov 29 2023 10:38:34
%S 1,0,8,52,240,1004,4072,16356,65504,262108,1048536,4194260,16777168,
%T 67108812,268435400,1073741764,4294967232,17179869116,68719476664,
%U 274877906868,1099511627696,4398046511020,17592186044328,70368744177572,281474976710560,1125899906842524
%N a(n) = 4^n - 4*n.
%C Numbers a(n)=k such that number m with n 4's and k 1's has digit product = digit sum = 4^n.
%H <a href="/index/Rec"order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4).
%F a(0)=1, a(1)=0, a(2)=8, a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3). - _Harvey P. Dale_, Oct 21 2011
%F G.f.: (-17*x^2+6*x-1)/((x-1)^2*(4 x-1)). - _Harvey P. Dale_, Oct 21 2011
%e Corresponding numbers m are 1, 4, 1111111144, ...
%t Table[4^m-4*m, {m, 0, 20}]
%t LinearRecurrence[{6,-9,4},{1,0,8},30] (* _Harvey P. Dale_, Oct 21 2011 *)
%o (Magma) [(4^n - 4*n): n in [0..25]]; // _Vincenzo Librandi_, Dec 16 2010
%o (PARI) a(n)=4^n-4*n \\ _Charles R Greathouse IV_, Sep 08 2012
%o (Python)
%o def A107584(n): return (1<<(n<<1))-(n<<2) # _Chai Wah Wu_, Nov 29 2023
%Y Cf. A107583, A107585.
%K nonn,easy
%O 0,3
%A _Zak Seidov_, May 16 2005
%E More terms from _Vincenzo Librandi_, Dec 16 2010
%E Corrected by _Charles R Greathouse IV_, Sep 08 2012
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