A192370 - OEIS

%I #24 Jul 06 2017 01:37:04

%S 20,880,35520,1422080,56888320,2275553280,91022213120,3640888852480,

%T 145635555409920,5825422221639680,233016888886558720,

%U 9320675555546234880,372827022222184939520,14913080888888739758080,596523235555554959032320,23860929422222219836129280

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

%C A192107 is the similar sequence when all the digits are odd.

%C A220094 is the similar sequence with the digits belonging to {1, 2, 3, 4, 5, 6, 7, 8, 9}.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (44,-160).

%F a(n) = (5 * 4^n * (10^n-1))/9.

%F From _Colin Barker_, Jan 04 2013: (Start)

%F a(n) = 44*a(n-1) - 160*a(n-2).

%F G.f.: 20*x/((4*x-1)*(40*x-1)). (End)

%e a(1) = 2 + 4 + 6 + 8 = 20.

%e a(2) = 22 + 24 + 26 + 28 + 42 + ... + 68 + 82 + 84 + 86 + 88 = 880.

%p A:=seq(5 * 4^n *(10^n-1)/9,n=1..20);

%t Table[(5*4^n*(10^n - 1))/9, {n, 20}] (* _T. D. Noe_, Dec 31 2012 *)

%o (PARI) a(n)=(5*4^n*(10^n-1))/9 \\ _Charles R Greathouse IV_, Jul 06 2017

%Y Cf. A192107, A220094, A045926.

%K nonn,base,easy

%O 1,1

%A _Bernard Schott_, Dec 31 2012