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 1-3 of 3 results.

A114140 Number of ordered sequences of coins (each of which has value 1, 2, 5, 10 or 20) which add to n.

Original entry on oeis.org

1, 1, 2, 3, 5, 9, 15, 26, 44, 75, 129, 220, 377, 644, 1101, 1883, 3219, 5505, 9412, 16093, 27518, 47051, 80453, 137563, 235215, 402188, 687688, 1175860, 2010567, 3437810, 5878212, 10050981, 17185883, 29385638, 50245647, 85913568, 146901103, 251181919
Offset: 0

Views

Author

David S. Johnson and N. J. A. Sloane, Feb 22 2006

Keywords

Comments

Equivalently, number of sequences of coins (each of which has value 5, 10, 25, 50 or 100) which add to 5n.
Based on "silver" US coins as of Feb 22 2006.
Number of compositions of n into parts 1, 2, 5, 10, and 20. - Joerg Arndt, Sep 19 2014

Crossrefs

Cf. A073031, A114044, A114138.

Programs

  • Maple
    A114140 := proc(n)
    coeftayl( 1/(1-(x+x^2+x^5+x^10+x^20)), x=0, n);
end proc:
seq(A114140(n), n=0..30); # Wesley Ivan Hurt, Sep 18 2014
  • Mathematica
    CoefficientList[Series[1/(1 - (x + x^2 + x^5 + x^10 + x^20)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 18 2014 *)

Formula

G.f.: 1/(1-(x+x^2+x^5+x^10+x^20)).

A114138 Number of (ordered) sequences of coins (each of which has value 1, 2, 5, 10, 20, 50, 100 or 200) which add to n.

Original entry on oeis.org

1, 1, 2, 3, 5, 9, 15, 26, 44, 75, 129, 220, 377, 644, 1101, 1883, 3219, 5505, 9412, 16093, 27518, 47051, 80453, 137563, 235215, 402188, 687688, 1175860, 2010567, 3437810, 5878212, 10050981, 17185883, 29385638, 50245647, 85913568, 146901103, 251181919
Offset: 0

Views

Author

David S. Johnson and N. J. A. Sloane, Feb 22 2006

Keywords

Comments

Based on Euro coins as of Feb 22 2006.

Crossrefs

Cf. A114044, A073031, A114140.

Programs

  • Mathematica
    CoefficientList[Series[1/(1-(x+x^2+x^5+x^10+x^20+x^50+x^100+x^200)),{x,0,50}],x] (* Harvey P. Dale, Nov 18 2013 *)

Formula

G.f.: 1/(1-(x+x^2+x^5+x^10+x^20+x^50+x^100+x^200)).

A351724 Number of compositions of n into parts of size 1, 5, 10 or 25.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 9, 13, 18, 24, 31, 42, 58, 80, 109, 146, 197, 268, 366, 499, 676, 916, 1243, 1690, 2299, 3122, 4237, 5751, 7811, 10614, 14418, 19580, 26587, 36106, 49043, 66614, 90473, 122869, 166866, 226632, 307810, 418060, 567784, 771122, 1047296, 1422396, 1931845
Offset: 0

Views

Author

R. J. Mathar, Feb 17 2022

Keywords

Comments

Starts to differ from A114044 at n=50.

Examples

			a(8)=5 counts 5 compositions 1+1+1+1+1+1+1+1 = 1+1+1+5 = 1+1+5+1 = 1+5+1+1 = 5+1+1+1.

Links

Crossrefs

Cf. A114044 (parts 50 and 100 admitted), A001299 (partitions).
Row sums of A351726.

Formula

G.f. : 1/(1-x-x^5-x^10-x^25).
a(n) = +a(n-1) +a(n-5) +a(n-10) +a(n-25).
Showing 1-3 of 3 results.

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

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