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 1-8 of 8 results.

A162521 Magic numbers A018226 divided by 2.

Original entry on oeis.org

1, 4, 10, 14, 25, 41, 63
Offset: 1

Views

Author

Omar E. Pol, Jul 06 2009

Keywords

Comments

Sequence related to atomic nuclei.

Crossrefs

Cf. A018226, A130517, A130556, A130598, A130602, A162522, A162523, A162524, A162525.

A162523 First differences of magic numbers A018226, divided by 2.

Original entry on oeis.org

3, 6, 4, 11, 16, 22
Offset: 1

Views

Author

Omar E. Pol, Jul 06 2009

Keywords

Comments

Sequence related to atomic nucleus.

Crossrefs

Cf. A018226, A130517, A130556, A130598, A130602, A162521, A162522, A162524, A162525.

Formula

a(n) = A162522(n)/2.

A162524 Partial sums of magic numbers A018226.

Original entry on oeis.org

2, 10, 30, 58, 108, 190, 316
Offset: 1

Views

Author

Omar E. Pol, Jul 06 2009

Keywords

Comments

Sequence related to atomic nuclei.

Crossrefs

Cf. A018226, A130517, A130556, A130598, A130602, A162521, A162522, A162523, A162525.

Extensions

Edited by Omar E. Pol, Jul 16 2009

A162525 Partial sums of magic numbers A018226, divided by 2.

Original entry on oeis.org

1, 5, 15, 29, 54, 95, 158
Offset: 1

Views

Author

Omar E. Pol, Jul 06 2009

Keywords

Comments

Sequence related to atomic nuclei.

Crossrefs

Cf. A018226, A130517, A130556, A130598, A130602, A162521, A162522, A162523, A162524.

Formula

a(n) = A162524(n)/2.

A162518 Characteristic function of magic numbers A018226: 1 if n is a magic number else 0.

Original entry on oeis.org

0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
Offset: 1

Views

Author

Omar E. Pol, Jul 07 2009

Keywords

Comments

Sequence related to atomic nuclei.

Links

Crossrefs

Cf. A018226, A130517, A130556, A130598, A130602, A162519, A162521, A162522, A162523, A162524, A162525.

Programs

Extensions

Data section extended up to a(126) by Antti Karttunen, Dec 24 2018

A162626 If 0 <= n <= 3 then a(n) = n(n+1)(n+2)/3, if n >= 4 then a(n) = n(n^2+5)/3.

Original entry on oeis.org

0, 2, 8, 20, 28, 50, 82, 126, 184, 258, 350, 462, 596, 754, 938, 1150, 1392, 1666, 1974, 2318, 2700, 3122, 3586, 4094, 4648, 5250, 5902, 6606, 7364, 8178, 9050, 9982, 10976, 12034, 13158, 14350, 15612, 16946, 18354, 19838, 21400, 23042, 24766, 26574
Offset: 0

Views

Author

Omar E. Pol, Jul 07 2009, Jul 13 2009

Keywords

Comments

One way to generalize the magic number sequence in A018226.
See also A130598 and A162630.

Crossrefs

Cf. A007290, A018226, A033547, A130598, A162518, A162519, A162521, A162522, A162523, A162524, A162525, A162630.

Formula

From Daniel Forgues, May 03 2011: (Start)
If 0 <= n <= 3 then a(n) = 2 T_n, otherwise a(n) = 2 (T_n - t_{n-1}), where T_n is the n-th tetrahedral number, t_n the n-th triangular number.
G.f.: (2*x*(1 - 6*x^3 + 14*x^4 - 11*x^5 + 3*x^6))/(1 - x)^4, n >= 0.
(End)
a(n) = n*(n^2+5)/3 + (4*n-6)*A171386(n). - Omar E. Pol, Aug 14 2013

Extensions

Edited by N. J. A. Sloane, Jul 18 2009

A162519 Characteristic function of magic numbers A018226: 0 if n is a magic number else 1.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Omar E. Pol, Jul 07 2009

Keywords

Comments

Also, successive digits of A130598.
This sequence is related to atomic nuclei. See also A162518.

Links

Crossrefs

Cf. A018226, A130517, A130556, A130598, A130602, A162518, A162521, A162522, A162523, A162524, A162525.

A210842 Number of states in the n-th shell of the nuclear shell model.

Original entry on oeis.org

2, 6, 12, 8, 22, 32, 44, 58
Offset: 1

Views

Author

Omar E. Pol, Jun 04 2012

Keywords

Comments

Partial sums of the first seven terms give the "magic numbers" A018226.
Also the partial sums of the first eight terms give the positive first eight terms of A162626 (and possibly more).

References

  • M. Goeppert Mayer and J. Hans D. Jensen, Elementary Theory of Nuclear Shell Structure, J. Wiley and Sons, Inc. (1955).
  • I. Talmi, Simple Models of Complex Nuclei, Hardwood Academic Publishers (1993).

Crossrefs

Row sums of triangle A212122.
Cf. A018226, A130517, A162522, A162626, A162630, A212121, A212123, A212124, A213361-A213364.
Showing 1-8 of 8 results.

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

Content is available under The OEIS End-User License Agreement.