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

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}.

Links

Table of n, a(n) for n=1..16.

Index entries for linear recurrences with constant coefficients, signature (44,-160).

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

Cf. A192107, A220094, A045926.

Sequence in context: A006424 A291112 A362168 * A113102 A285673 A250017

Adjacent sequences: A192367 A192368 A192369 * A192371 A192372 A192373

Keyword

nonn,base,easy

Author

Bernard Schott, Dec 31 2012

Status

approved