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.

A036090 Centered cube numbers: (n+1)^12 + n^12.

Original entry on oeis.org

1, 4097, 535537, 17308657, 260917841, 2420922961, 16018069537, 82560763937, 351149013217, 1282429536481, 4138428376721, 12054528824977, 32214185570737, 79991997497777, 186440250265921, 411221314601281
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Never prime, as a(n) = (2n^4 + 4n^3 + 6n^2 + 4n + 1) * (n^8 + 4n^7 + 22n^6 + 52n^5 + 69n^4 + 56n^3 + 28n^2 + 8n + 1) Semiprime for n in {1, 2, 3, 6, 14, 16, 36, 87, 97, 109, 110, 119, 121, 163, 195, ...}. - Jonathan Vos Post, Aug 26 2011

References

  • B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Links

Crossrefs

Cf. A008456, A036088, A036089, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

Programs

  • Magma
    [(n+1)^12+n^12: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011
  • Mathematica
    Total/@Partition[Range[0,20]^12,2,1] (* Harvey P. Dale, May 09 2018 *)

Formula

G.f.: -(x^10 + 4082*x^9 + 474189*x^8 + 9713496*x^7 + 56604978*x^6 + 105907308*x^5 + 56604978*x^4 + 9713496*x^3 + 474189*x^2 + 4082*x + 1)*(1+x)^2 / (x-1)^13. - R. J. Mathar, Aug 27 2011

A036091 Centered cube numbers: (n+1)^13+n^13.

Original entry on oeis.org

1, 8193, 1602515, 68703187, 1287811989, 14281397141, 109949704423, 646644824295, 3091621642217, 12541865828329, 44522712143931, 141515917523003, 409868311971325, 1096589879846397, 2739909841613519
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Never prime, as a(n) = (2n + 1) * (n^12 + 6n^11 + 36n^10 + 125n^9 + 295n^8 + 496n^7 + 610n^6 + 553n^5 + 367n^4 + 174n^3 + 56n^2 + 11n + 1). Semiprime for n in {1, 8, 15, 21, 86, 135, 141, 249, 260, 278, 323, 326, 363, ...}. - Jonathan Vos Post, Aug 26 2011

Links

Crossrefs

Cf. A036085, A036087, A036088, A036089, A036090.

Programs

A036092 Centered cube numbers: a(n) = (n+1)^14 + n^14.

Original entry on oeis.org

1, 16385, 4799353, 273218425, 6371951081, 84467679721, 756587236945, 5076269583953, 27274838966065, 122876792454961, 479749833583241, 1663668298132105, 5221294850248153, 15049383211257305, 40304932850948641, 101250520063318561, 240435420597328865
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Never prime, as a(n) = (2n^2 + 2n + 1) * (n^12 + 6n^11 + 39n^10 + 140n^9 + 341n^8 + 590n^7 + 741n^6 + 680n^5 + 451n^4 + 210n^3 + 65n^2 + 12n + 1). Semiprime for n in {2, 5, 22, 24, 34, 35, 39, 84, 217, 220, 285, ...}. - Jonathan Vos Post, Aug 26 2011

Links

Crossrefs

Cf. A000040, A036085, A036087, A036088, A036089, A036090, A036091, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

Programs

Formula

G.f.: -(x +1)^2*(x^12 +16368*x^11 +4520946*x^10 +193889840*x^9 +2377852335*x^8 +10465410528*x^7 +17505765564*x^6 +10465410528*x^5 +2377852335*x^4 +193889840*x^3 +4520946*x^2 +16368*x +1) / (x -1)^15. - Colin Barker, Feb 16 2015

A036095 Centered cube numbers: a(n) = (n+1)^17 + n^17.

Original entry on oeis.org

1, 131073, 129271235, 17309009347, 780119322309, 17689598897861, 249557173431943, 2484430327672455, 18928981513351817, 116677181699666569, 605447028499293771, 2724058135239730763, 10869027026121774925
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Never prime, as a(n) = (2n + 1) * (n^16 + 8n^15 + 64n^14 + 308n^13 + 1036n^12 + 2576n^11 + 4900n^10 + 7274n^9 + 8518n^8 + 7896n^7 + 5776n^6 + 3300n^5 + 1444n^4 + 468n^3 + 106n^2 + 15n + 1). Semiprime for n in {1, 5, 21, 29, 33, ...}. - Jonathan Vos Post, Aug 27 2011

References

  • B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Links

Crossrefs

Cf. A000040, A036085, A036087, A036088, A036089, A036090, A036091, A036092, A036093, A100267, A154535, A100266, A152913, A194155, A194185, A194216.

Programs

Showing 1-4 of 4 results.

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

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