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A192370 Sum of all the n-digit numbers whose digits are all even and nonzero: 2,4,6,8.

%I A192370 #24 Jul 06 2017 01:37:04
%S A192370 20,880,35520,1422080,56888320,2275553280,91022213120,3640888852480,
%T A192370 145635555409920,5825422221639680,233016888886558720,
%U A192370 9320675555546234880,372827022222184939520,14913080888888739758080,596523235555554959032320,23860929422222219836129280
%N A192370 Sum of all the n-digit numbers whose digits are all even and nonzero: 2,4,6,8.
%C A192370 A192107 is the similar sequence when all the digits are odd.
%C A192370 A220094 is the similar sequence with the digits belonging to {1, 2, 3, 4, 5, 6, 7, 8, 9}.
%H A192370 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (44,-160).
%F A192370 a(n) = (5 * 4^n * (10^n-1))/9.
%F A192370 From _Colin Barker_, Jan 04 2013: (Start)
%F A192370 a(n) = 44*a(n-1) - 160*a(n-2).
%F A192370 G.f.: 20*x/((4*x-1)*(40*x-1)). (End)
%e A192370 a(1) = 2 + 4 + 6 + 8 = 20.
%e A192370 a(2) = 22 + 24 + 26 + 28 + 42 + ... + 68 + 82 + 84 + 86 + 88 = 880.
%p A192370 A:=seq(5 * 4^n *(10^n-1)/9,n=1..20);
%t A192370 Table[(5*4^n*(10^n - 1))/9, {n, 20}] (* _T. D. Noe_, Dec 31 2012 *)
%o A192370 (PARI) a(n)=(5*4^n*(10^n-1))/9 \\ _Charles R Greathouse IV_, Jul 06 2017
%Y A192370 Cf. A192107, A220094, A045926.
%K A192370 nonn,base,easy
%O A192370 1,1
%A A192370 _Bernard Schott_, Dec 31 2012