A179819 Monetary amounts in U.S. cents such that the smallest number of coins summing to the amount uses only denominations of 10 cents and above.

10, 20, 25, 35, 45, 50, 60, 70, 75, 85, 95, 100, 110, 120, 125, 135, 145, 150, 160, 170, 175, 185, 195, 200, 210, 220, 225, 235, 245, 250, 260, 270, 275, 285, 295, 300, 310, 320, 325, 335, 345, 350, 360, 370, 375, 385, 395, 400, 410, 420, 425, 435, 445, 450, 460, 470, 475, 485, 495, 500, 510, 520, 525, 535, 545, 550, 560

Offset

1,1

Comments

U.S. coins are the cent ("penny") (1 cent), nickel (5 cents), dime (10 cents), quarter dollar ("quarter") (25 cents), half dollar (50 cents), and dollar (100 cents).

For values above 100, one can simply add 100 to the previous terms: a(n) = a(n-12) + 100. - R. J. Mathar, Aug 05 2010

Links

Table of n, a(n) for n=1..67.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

From R. J. Mathar, Aug 05 2010: (Start)

a(n) = +a(n-1) +a(n-3) -a(n-4).

G.f.: 5*x*(2+2*x+x^2) / ( (1+x+x^2)*(x-1)^2 ). (End)

Example

A total amount of 30 cents can be obtained using 3 coins as 10+10+10, but the only way to obtain 30 cents using 2 coins (which is the minimum number of coins) is as 25+5 (which includes a coin smaller than a 10-cent piece), so 30 is not in the sequence.
From R. J. Mathar, Aug 05 2010: (Start)
Shortest partitions of multiples of 5 into parts of 5, 10, 25, 50, 100:
    5 =   5
   10 =  10                  a(1)
   15 =   5 + 10
   20 =  10 + 10             a(2)
   25 =  25                  a(3)
   30 =   5 + 25
   35 =  10 + 25             a(4)
   40 =   5 + 10 + 25
   45 =  10 + 10 + 25        a(5)
   50 =  50                  a(6)
   55 =   5 + 50
   60 =  10 + 50             a(7)
   65 =   5 + 10 + 50
   70 =  10 + 10 + 50        a(8)
   75 =  25 + 50             a(9)
   80 =   5 + 25 + 50
   85 =  10 + 25 + 50        a(10)
   90 =   5 + 10 + 25 + 50
   95 =  10 + 10 + 25 + 50   a(11)
  100 = 100.                 a(12)
(End)

Crossrefs

Sequence in context: A034048 A199978 A342142 * A320522 A072592 A229305

Adjacent sequences: A179816 A179817 A179818 * A179820 A179821 A179822

Keyword

nonn,easy

Author

J. Lowell, Jul 28 2010

Extensions

More terms from R. J. Mathar, Aug 05 2010

More terms from Max Alekseyev, Oct 15 2012

Status

approved