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.

A087348 a(n) = 10*n^2 - 6*n + 1.

Original entry on oeis.org

5, 29, 73, 137, 221, 325, 449, 593, 757, 941, 1145, 1369, 1613, 1877, 2161, 2465, 2789, 3133, 3497, 3881, 4285, 4709, 5153, 5617, 6101, 6605, 7129, 7673, 8237, 8821, 9425, 10049, 10693, 11357, 12041, 12745, 13469, 14213, 14977, 15761, 16565, 17389, 18233, 19097
Offset: 1

Views

Author

Charlie Marion, Oct 20 2003

Keywords

Comments

Sequence found by reading the line from 5, in the direction 5, 29, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Jul 18 2012

Examples

			a(3)=73 since 73^2 = 48^2 + 55^2 = (4*12)^2 + (48 + 7)^2. See 1st formula.

Links

Crossrefs

Cf. A000326, A033567, A033579, A056220, A085787, A153784.

Programs

Formula

a(n)^2 = A033579(n)^2 + A033567(n)^2 = (4*A000326(n))^2 + (A033579(n) + A056220(n-1))^2.
From Colin Barker, Jun 30 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(5 + 14*x + x^2)/(1-x)^3. (End)
a(n) = 1 + A153784(n). - Omar E. Pol, Jul 18 2012
E.g.f.: exp(x)*(10*x^2 + 4*x + 1) - 1. - Elmo R. Oliveira, Oct 31 2024

Extensions

More terms from Ray Chandler, Oct 22 2003

A153785 5 times heptagonal numbers: a(n) = 5*n*(5*n-3)/2.

Original entry on oeis.org

0, 5, 35, 90, 170, 275, 405, 560, 740, 945, 1175, 1430, 1710, 2015, 2345, 2700, 3080, 3485, 3915, 4370, 4850, 5355, 5885, 6440, 7020, 7625, 8255, 8910, 9590, 10295, 11025, 11780, 12560, 13365, 14195, 15050, 15930, 16835, 17765
Offset: 0

Views

Author

Omar E. Pol, Jan 07 2009

Keywords

Links

Crossrefs

Cf. A000566, A153784, A154786.

Programs

  • Mathematica
    s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,5,8!,25}];lst (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *)
Table[5*n*(5*n - 3)/2, {n,0,25}] (* or *) LinearRecurrence[{3,-3,1}, {0,5,35}, 25] (* G. C. Greubel, Aug 28 2016 *)
  • PARI
    a(n) = 5*n*(5*n-3)/2; \\ Michel Marcus, Aug 28 2016

Formula

a(n) = (25*n^2 - 15*n)/2 = A000566(n)*5.
a(n) = 25*n + a(n-1) - 20 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
From G. C. Greubel, Aug 28 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: 5*x*(1 + 4*x)/(1 - x)^3.
E.g.f.: (5/2)*x*(2 + 5*x)*exp(x). (End)
Showing 1-2 of 2 results.

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