login
This site is supported by donations to The OEIS Foundation.

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A067997 Number of (unordered) ways of making change for n cents using coins of 1/2, 1, 2, 3, 5, 10, 20, 25, 50, 100 cents (all historical U.S.A. coinage denominations up to 100 cents). 4
1, 2, 4, 7, 11, 17, 25, 35, 48, 64, 85, 110, 141, 178, 222, 275, 337, 409, 493, 589, 702, 830, 977, 1144, 1333, 1549, 1792, 2065, 2372, 2714, 3100, 3528, 4005, 4534, 5119, 5769, 6485, 7273, 8140, 9089, 10135, 11276, 12524, 13885, 15366, 16983, 18738 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The U.S.A. issued the following unusual denomination coins during the 18th and 19th centuries: 1/2-cent pieces, 1793-1857; 2-cent pieces, 1864-1873; 3-cent pieces, 1851-1889; and 20-cent pieces, 1875-1878. This sequence is also the number of ways of making change for n cents using coins of 1 (two types, say, old pre-1858 "large cents" and 1856-to-present "small cents"), 2, 3, 5, 10, 20, 25, 50, 100 cents. For present purposes, one of the two types of 1-cent piece is actually taken to be two 1/2-cent pieces.

REFERENCES

R. S. Yeoman, A Guide Book of United States Coins, Ed. Kenneth Bressett, 53rd Edition (2000). New York: St. Martin's Press, 1999. pp. 72-77, 92-93, 104-106, 135. (also known as The Official Red Book of United States Coins)

LINKS

Table of n, a(n) for n=0..46.

Ron Guth, Your Online Reference For U.S. Coins

Mitch Hight, United States Coinage History

Clint Leland, U.S. Coins Quantities Minted

Index entries for sequences related to making change.

FORMULA

G.f.: 1/((1-x)^2*(1-x^2)*(1-x^3)*(1-x^5)*(1-x^10)*(1-x^20)*(1-x^25)*(1-x^50)*(1-x^100))

EXAMPLE

a(2)=4 because change can be made for 2 cents in these 4 ways: (1) 4 1/2-cent coins, (2) 2 1/2-cent, 1 1-cent, (3) 2 1-cent, (4) 1 2-cent coin.

MATHEMATICA

CoefficientList[ Series[1 / ((1 - x)^2(1 - x^2)(1 - x^3)(1 - x^5)(1 - x^10)(1 - x^20)(1 - x^25)(1 - x^50)(1 - x^100)), {x, 0, 50} ], x]

PROG

(PARI) a(n)=polcoeff(1/((1-x)^2*(1-x^2)*(1-x^3)*(1-x^5)*(1-x^10)*(1-x^20)*(1-x^25)*(1-x^50)*(1-x^100)+x*O(x^n)), n)

CROSSREFS

Cf. A067996, A067995, A001314 (two kinds of nickels), A028291 (analog for 1/2, 1, 2, 3, 5 only, or 1(two types), 2, 3, 5 only).

Sequence in context: A266901 A117649 A028291 * A175491 A034379 A007000

Adjacent sequences:  A067994 A067995 A067996 * A067998 A067999 A068000

KEYWORD

easy,nonn

AUTHOR

Rick L. Shepherd, Feb 08 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 18 22:18 EDT 2017. Contains 290768 sequences.