A220094 -id:A220094 - cp's OEIS frontend

A192107 Sum of all the n-digit numbers whose digits are all odd.

25, 1375, 69375, 3471875, 173609375, 8680546875, 434027734375, 21701388671875, 1085069443359375, 54253472216796875, 2712673611083984375, 135633680555419921875, 6781684027777099609375, 339084201388885498046875, 16954210069444427490234375

Offset: 1

Bernard Schott, Dec 30 2012

The idea for this sequence comes from question 4 of the Final Round of the Finnish High School Mathematics Contest in 1997 (see link IMO Compendium and Crux reference) where the question was asked regarding only 4-digit numbers.
A192370 is the similar sequence when all the digits are even: 2, 4, 6, 8.
A220094 is the similar sequence with the digits belonging to {1, 2, 3, 4, 5, 6, 7, 8, 9}.

			a(1) = 1 + 3 + 5 + 7 + 9 = 25.
a(2) = 11 + 13 + ... + 19 + 31 + ... + 79 + 91 + ... + 99 = 1375.

Finnish High School Mathematics Contest, Final Round, 1997, problem 4. [Crux Mathematicorum, v22 n3, Apr. 2002, p. 143]

The IMO compendium, Problem 4, Finnish High School Mathematics Contest 1997.
Index entries for linear recurrences with constant coefficients, signature (55,-250).
Index to sequences related to Olympiads.

Cf. A220094, A192370, A014261.

Maple
```
A:=seq((10^n-1)*5^(n+1)/9,n=1..20);
```

Table[((10^n - 1)*5^(n + 1))/9, {n, 20}] (* T. D. Noe, Dec 31 2012 *)
LinearRecurrence[{55,-250},{25,1375},20] (* Harvey P. Dale, Oct 11 2018 *)

a(n) = (10^n-1) * 5^(n+1)/9 \\ Charles R Greathouse IV, Jul 06 2017

a(n) = ((10^n-1) * 5^(n+1))/9 = 5^(n+1) * R_n with R_n is the repunit with n times the digit 1.
From Colin Barker, Jan 04 2013: (Start)
a(n) = 55*a(n-1) - 250*a(n-2).
G.f.: 25*x/((5*x-1)*(50*x-1)). (End)

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

Original entry on oeis.org

20, 880, 35520, 1422080, 56888320, 2275553280, 91022213120, 3640888852480, 145635555409920, 5825422221639680, 233016888886558720, 9320675555546234880, 372827022222184939520, 14913080888888739758080, 596523235555554959032320, 23860929422222219836129280

Offset: 1

Bernard Schott, Dec 31 2012

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}.

			a(1) = 2 + 4 + 6 + 8 = 20.
a(2) = 22 + 24 + 26 + 28 + 42 + ... + 68 + 82 + 84 + 86 + 88 = 880.

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

Cf. A192107, A220094, A045926.

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

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

a(n)=(5*4^n*(10^n-1))/9 \\ Charles R Greathouse IV, Jul 06 2017

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)

cp's OEIS Frontend

A192107 Sum of all the n-digit numbers whose digits are all odd.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula