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.

A047667 Row 3 of array in A047666.

Original entry on oeis.org

3, 10, 25, 52, 95, 158, 245, 360, 507, 690, 913, 1180, 1495, 1862, 2285, 2768, 3315, 3930, 4617, 5380, 6223, 7150, 8165, 9272, 10475, 11778, 13185, 14700, 16327, 18070, 19933, 21920, 24035, 26282, 28665, 31188, 33855, 36670, 39637, 42760, 46043, 49490, 53105
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A047666, A192793.

Programs

  • PARI
    my(x='x+O('x^44)); Vec(x*(3-2*x+3*x^2)/(x-1)^4) \\ Elmo R. Oliveira, Aug 26 2025

Formula

a(n) = (n/3)*(2*n^2 + 7).
From Elmo R. Oliveira, Aug 26 2025: (Start)
G.f.: x*(3 - 2*x + 3*x^2)/(x - 1)^4.
E.g.f.: x*(9 + 6*x + 2*x^2)*exp(x)/3.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4.
a(n) = A192793(n)/36. (End)

Extensions

More terms from Elmo R. Oliveira, Aug 26 2025

A047668 Row 4 of array in A047666.

Original entry on oeis.org

4, 17, 52, 129, 276, 529, 932, 1537, 2404, 3601, 5204, 7297, 9972, 13329, 17476, 22529, 28612, 35857, 44404, 54401, 66004, 79377, 94692, 112129, 131876, 154129, 179092, 206977, 238004, 272401, 310404, 352257, 398212, 448529
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

In this sequence if we do a forward difference, then the 3rd forward difference when considered as a sequence will be an arithmetic progression with common difference 8. [Gopalakrishnan (gopala498(AT)yahoo.co.in), Jun 05 2010]

Links

Programs

  • Mathematica
    LinearRecurrence[{5,-10,10,-5,1},{4,17,52,129,276},40] (* Harvey P. Dale, Jul 05 2024 *)

Formula

a(n) = (1/3) * (n^4 + 8n^2 + 3).
G.f.: x*(4 - 3*x + 7*x^2 - x^3 + x^4)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009 [corrected by R. J. Mathar, Sep 16 2009]

A047670 Row 6 of array in A047666.

Original entry on oeis.org

6, 37, 158, 529, 1486, 3653, 8086, 16449, 31222, 55941, 95470, 156305, 246910, 378085, 563366, 819457, 1166694, 1629541, 2237118, 3023761, 4029614, 5301253, 6892342, 8864321, 11287126, 14239941, 17811982, 22103313, 27225694, 33303461, 40474438, 48890881
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Programs

  • Mathematica
    LinearRecurrence[{7,-21,35,-35,21,-7,1},{6,37,158,529,1486,3653,8086},40] (* Harvey P. Dale, Jun 15 2018 *)
  • PARI
    Vec(-x*(x^6-x^5+16*x^4-10*x^3+25*x^2-5*x+6)/(x-1)^7 + O(x^100)) \\ Colin Barker, Nov 24 2014

Formula

a(n) = (1/45) * (2n^6 + 50n^4 + 173 + 45).
G.f.: -x*(x^6 - x^5 + 16*x^4 - 10*x^3 + 25*x^2 - 5*x + 6) / (x-1)^7. - Colin Barker, Nov 24 2014

Extensions

More terms from Colin Barker, Nov 24 2014

A047669 Row 5 of array in A047666.

Original entry on oeis.org

5, 26, 95, 276, 681, 1486, 2947, 5416, 9357, 15362, 24167, 36668, 53937, 77238, 108043, 148048, 199189, 263658, 343919, 442724, 563129, 708510, 882579, 1089400, 1333405, 1619410, 1952631, 2338700, 2783681, 3294086, 3876891, 4539552, 5290021, 6136762, 7088767
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Programs

  • Mathematica
    Table[(n/15)(2n^4+30n^2+43),{n,40}]  (* Harvey P. Dale, May 25 2023 *)

Formula

a(n) = (n/15) * (2n^4 + 30n^2 + 43).
G.f.: x*(5*x^4-4*x^3+14*x^2-4*x+5)/(x-1)^6.
Showing 1-4 of 4 results.

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

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