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 1-2 of 2 results.

A053742 Sum of odd numbers in range 10*n to 10*n+9.

Original entry on oeis.org

25, 75, 125, 175, 225, 275, 325, 375, 425, 475, 525, 575, 625, 675, 725, 775, 825, 875, 925, 975, 1025, 1075, 1125, 1175, 1225, 1275, 1325, 1375, 1425, 1475, 1525, 1575, 1625, 1675, 1725, 1775, 1825, 1875, 1925, 1975, 2025, 2075, 2125, 2175, 2225, 2275
Offset: 0

Views

Author

Odimar Fabeny, Feb 13 2000

Keywords

Comments

Integers that are the product of two integers ending with 5. - Michel Marcus, Mar 16 2019

Examples

			25 = 1+3+5+7+9; 75 = 11+13+15+17+19; ...

Links

Crossrefs

Cf. A053741, A053743.

Programs

Formula

a(n) = 25 + 50*n.
a(n) = a(n-1) + 50. - Harvey P. Dale, Aug 11 2011
From Colin Barker, Jun 27 2012: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: 25*(1+x)/(1-x)^2. (End)
E.g.f.: 25*(1+2*x)*exp(x). - G. C. Greubel, Sep 06 2019

Extensions

More terms from James Sellers, Feb 22 2000

A053743 Sum of numbers in range 10*n to 10*n+9.

Original entry on oeis.org

45, 145, 245, 345, 445, 545, 645, 745, 845, 945, 1045, 1145, 1245, 1345, 1445, 1545, 1645, 1745, 1845, 1945, 2045, 2145, 2245, 2345, 2445, 2545, 2645, 2745, 2845, 2945, 3045, 3145, 3245, 3345, 3445, 3545, 3645, 3745, 3845, 3945, 4045, 4145, 4245, 4345
Offset: 0

Views

Author

Odimar Fabeny, Feb 13 2000

Keywords

Examples

			45 = sum of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9;
145 = sum of 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.

Links

Crossrefs

Cf. A053741, A053742.

Programs

  • GAP
    List([0..50], n-> 5*(20*n+9)); # G. C. Greubel, Sep 06 2019
  • Magma
    [5*(20*n+9): n in [0..50]]; // G. C. Greubel, Sep 06 2019
  • Maple
    seq(5*(20*n+9), n=0..50); # G. C. Greubel, Sep 06 2019
  • Mathematica
    LinearRecurrence[{2,-1},{45,145},50] (* or *) 100*Range[50]-55 (* Harvey P. Dale, Feb 03 2019 *)
  • PARI
    vector(50, n, 5*(20*n -11)) \\ G. C. Greubel, Sep 06 2019
  • Sage
    [5*(20*n+9) for n in (0..50)] # G. C. Greubel, Sep 06 2019

Formula

a(n) = 100*n + 45.
From Colin Barker, Jun 26 2012: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: 5*(9+11*x)/(1-x)^2. (End)
E.g.f.: 5*(9 + 20*x)*exp(x). - G. C. Greubel, Sep 06 2019

Extensions

More terms from James Sellers, Feb 22 2000
Showing 1-2 of 2 results.

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

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