cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A018283 Divisors of 100.

Original entry on oeis.org

1, 2, 4, 5, 10, 20, 25, 50, 100
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

From Alonso del Arte, Oct 10 2017: (Start)
There are just three ways to partition 100 into its distinct divisors: 100 = 50 + 25 + 20 + 5 = 50 + 25 + 20 + 4 + 1 (see A033630).
However, it's not possible to exchange a United States 1-dollar coin for smaller coins of distinct denominations in current circulation since there are no 4- or 20-cent coins (see A112024).
Nor is it possible to exchange a 100-dollar bill for smaller bills of distinct denominations as there are no 4- or 25-dollar bills (see A124146). (End)

Links

Crossrefs

This sequence is row n = 100 of A027750.

Programs

Formula

a(n) = 2^((n-1) mod 3)*5^floor((n-1)/3). - Aaron J Grech, Aug 11 2024

A135137 Numbers that are the sum of three numbers from the set {1, 5, 10, 20, 50, 100}.

Original entry on oeis.org

3, 7, 11, 12, 15, 16, 20, 21, 22, 25, 26, 30, 31, 35, 40, 41, 45, 50, 52, 56, 60, 61, 65, 70, 71, 75, 80, 90, 101, 102, 105, 106, 110, 111, 115, 120, 121, 125, 130, 140, 150, 151, 155, 160, 170, 200, 201, 205, 210, 220, 250, 300
Offset: 1

Views

Author

Julie Jones, Feb 13 2008

Keywords

Examples

			sum, n1..n6 (from _Zak Seidov_):
3, 3,0,0,0,0,0,
7, 2,1,0,0,0,0,
11, 1,2,0,0,0,0,
12, 2,0,1,0,0,0,
15, 0,3,0,0,0,0,
16, 1,1,1,0,0,0,
20, 0,2,1,0,0,0,
21, 1,0,2,0,0,0,
22, 2,0,0,1,0,0,
25, 0,1,2,0,0,0,
...

Crossrefs

Cf. A124146, A135454.

Programs

  • Mathematica
    Union[Total/@Tuples[{1,5,10,20,50,100},{3}]] (* Harvey P. Dale, Jan 11 2011 *)

Extensions

Edited by N. J. A. Sloane, Feb 18 2008

A135526 Number of sums payable using exactly n banknotes of denominations 1, 5, 10, 20, 50, 100 (change allowable).

Original entry on oeis.org

1, 6, 33, 95, 188, 288, 388, 488, 588, 688, 788, 888, 988, 1088, 1188, 1288, 1388, 1488, 1588, 1688, 1788, 1888, 1988, 2088, 2188, 2288, 2388, 2488, 2588, 2688, 2788, 2888, 2988, 3088, 3188, 3288, 3388, 3488, 3588, 3688, 3788, 3888, 3988, 4088, 4188, 4288
Offset: 0

Views

Author

Zak Seidov, Feb 20 2008

Keywords

Comments

Terms and formula from Max Alekseyev and Robert Israel.

Links

Crossrefs

Cf. A124146, A135137, A135454.

Programs

  • Mathematica
    Join[{1,6,33,95}, LinearRecurrence[{2,-1},{188,288},25]] (* or *) Join[{1,6,33,95}, Table[100*n -212, {n,4,25}]] (* G. C. Greubel, Oct 17 2016 *)
  • PARI
    a(n)=if(n>3,100*n-212,[1,6,33,95][n+1]) \\ Charles R Greathouse IV, Jun 23 2024

Formula

a(n) = 100*n - 212 for n>=4.
From G. C. Greubel, Oct 17 2016: (Start)
a(n) = 2*a(n-1) - a(n-2), for n >= 4.
G.f.: (1 + 4*x + 22*x^2 + 35*x^3 + 31*x^4 + 7*x^5)/(1-x)^2.
E.g.f.: (1/6)*( 1278 + 708*x + 135*x^2 + 7*x^3 - 24*(53 - 25*x)*exp(x) ). (End)

Extensions

Extended by Max Alekseyev, Mar 04 2009

A339094 Number of (unordered) ways of making change for n US Dollars using the current US denominations of $1, $2, $5, $10, $20, $50 and $100 bills.

Original entry on oeis.org

1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 11, 12, 15, 16, 19, 22, 25, 28, 31, 34, 41, 44, 51, 54, 61, 68, 75, 82, 89, 96, 109, 116, 129, 136, 149, 162, 175, 188, 201, 214, 236, 249, 271, 284, 306, 328, 350, 372, 394, 416, 451, 473, 508, 530, 565, 600, 635, 670, 705, 740, 793, 828, 881, 916
Offset: 0

Views

Author

Robert G. Wilson v, Nov 25 2020

Keywords

Comments

Not the same as A001313. First difference appears at A001313(100) being 4562, whereas a(100) is 4563; obviously one more than A001313(100).
Not the same as A057537.
Number of partitions of n into parts 1, 2, 5, 10, 20, 50 and 100.

Examples

			a(5) is 4 because 1+1+1+1+1 = 2+1+1+1 = 2+2+1 = 5.

Links

Crossrefs

Cf. A000008, A001299, A001300, A001301, A001306, A001302, A001306, A001310, A001312, A001313, A001314, A001319, A001343, A001362, A001364, A057537, A067996, A067997, A073031, A085502, A112024, A124146, A160551, A169718, A181934, A187243.

Programs

  • Mathematica
    f[n_] := Length@ IntegerPartitions[n, All, {1, 2, 5, 10, 20, 50, 100}]; Array[f, 75, 0] (* or *)
CoefficientList[ Series[1/((1 - x) (1 - x^2) (1 - x^5) (1 - x^10) (1 - x^20) (1 - x^50) (1 - x^100)), {x, 0, 75}], x] (* or *)
Table[ Length@ FrobeniusSolve[{1, 2, 5, 10, 20, 50, 100}, n], {n, 0, 75}] (* much slower *)
  • PARI
    coins(v[..])=my(x='x); prod(i=1, #v, 1/(1-x^v[i]))
Vec(coins(1, 2, 5, 10, 20, 50, 100)+O(x^99)) \\ Charles R Greathouse IV, Jan 24 2022

Formula

G.f.: 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^20)*(1-x^50)*(1-x^100)).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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