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URL: https://oeis.org/A192370

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A192370
Sum of all the n-digit numbers whose digits are all even and nonzero: 2,4,6,8.
3
20, 880, 35520, 1422080, 56888320, 2275553280, 91022213120, 3640888852480, 145635555409920, 5825422221639680, 233016888886558720, 9320675555546234880, 372827022222184939520, 14913080888888739758080, 596523235555554959032320, 23860929422222219836129280
OFFSET
1,1
COMMENTS
A192107 is the similar sequence when all the digits are odd.
A220094 is the similar sequence with the digits belonging to {1, 2, 3, 4, 5, 6, 7, 8, 9}.
FORMULA
a(n) = (5 * 4^n * (10^n-1))/9.
From Colin Barker, Jan 04 2013: (Start)
a(n) = 44*a(n-1) - 160*a(n-2).
G.f.: 20*x/((4*x-1)*(40*x-1)). (End)
EXAMPLE
a(1) = 2 + 4 + 6 + 8 = 20.
a(2) = 22 + 24 + 26 + 28 + 42 + ... + 68 + 82 + 84 + 86 + 88 = 880.
MAPLE
A:=seq(5 * 4^n *(10^n-1)/9, n=1..20);
MATHEMATICA
Table[(5*4^n*(10^n - 1))/9, {n, 20}] (* T. D. Noe, Dec 31 2012 *)
PROG
(PARI) a(n)=(5*4^n*(10^n-1))/9 \\ Charles R Greathouse IV, Jul 06 2017
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Bernard Schott, Dec 31 2012
STATUS
approved