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.

A290807 Number of partitions of n into Pell parts (A000129).

Original entry on oeis.org

1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 18, 20, 23, 26, 29, 32, 36, 39, 44, 47, 53, 57, 63, 68, 74, 81, 88, 95, 103, 110, 120, 128, 139, 148, 159, 170, 182, 195, 208, 221, 236, 250, 267, 282, 300, 317, 336, 355, 375, 396, 418, 440, 464, 487, 514, 539, 568, 595, 625, 655, 687, 720, 754, 788
Offset: 0

Views

Author

Ilya Gutkovskiy, Aug 11 2017

Keywords

Examples

			a(5) = 4 because we have [5], [2, 2, 1], [2, 1, 1, 1] and [1, 1, 1, 1, 1].

Links

Crossrefs

Cf. A000129, A007000, A003107, A067592, A067593, A290808.

Programs

  • Mathematica
    CoefficientList[Series[Product[1/(1 - x^Fibonacci[k, 2]), {k, 1, 15}], {x, 0, 67}], x]

Formula

G.f.: Product_{k>=1} 1/(1 - x^A000129(k)).

A294204 Number of partitions of n into distinct Lucas parts (A000032) greater than 1.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 1, 2, 0, 2, 1, 2, 1, 2, 2, 1, 2, 1, 3, 0, 3, 2, 2, 2, 2, 3, 0, 3, 1, 3, 1, 3, 3, 2, 3, 2, 4, 0, 4, 2, 3, 2, 3, 3, 1, 3, 1, 4, 0, 4, 3, 3, 3, 3, 5, 0, 5, 2, 4, 2, 4, 4, 2, 4, 2, 5, 0, 5, 3, 3, 3, 3, 4, 0, 4, 1, 4, 1, 4, 4, 3, 4, 3, 6, 0, 6, 3, 5, 3, 5, 5, 2, 5, 2, 6, 0, 6, 4, 4, 4, 4
Offset: 0

Views

Author

Ilya Gutkovskiy, Oct 24 2017

Keywords

Comments

Convolution of the sequences A067595 and A033999.

Examples

			a(9) = 2 because we have [7, 2] and [4, 3, 2].

Links

Crossrefs

Cf. A000032, A033999, A067593, A067595, A239002, A294203.

Programs

  • Mathematica
    CoefficientList[Series[(1 + x^2) Product[1 + x^LucasL[k], {k, 2, 15}], {x, 0, 100}], x]

Formula

G.f.: (1 + x^2)*Product_{k>=2} (1 + x^Lucas(k)).

A357306 Number of compositions (ordered partitions) of n into distinct Lucas numbers (beginning at 2).

Original entry on oeis.org

1, 1, 1, 3, 3, 4, 8, 9, 8, 8, 32, 9, 14, 32, 38, 32, 36, 150, 33, 32, 32, 158, 38, 60, 174, 176, 150, 150, 870, 33, 56, 152, 182, 158, 180, 894, 182, 174, 174, 1014, 176, 294, 990, 1014, 870, 888, 5904, 153, 152, 152, 902, 182, 300, 1014, 1022, 894, 894
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 23 2022

Keywords

Links

Crossrefs

Cf. A000032, A003263, A067593, A067595, A218396, A288039, A331922.

A357520 Expansion of Product_{k>=0} (1 - x^Lucas(k)).

Original entry on oeis.org

1, -1, -1, 0, 0, 2, 0, -1, 0, 0, 1, -1, -1, 1, 0, 1, -1, -1, 0, 1, 1, -1, 0, 0, 0, 1, -1, -1, 0, 0, 2, 0, 0, -1, -1, 1, 0, 0, 0, 0, 1, -1, -1, 0, 0, 2, 0, -1, 0, 0, 1, 0, -2, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 2, 0, -1, 0, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 0, -1, 0, 2, 0, 0, -1, -1, 1
Offset: 0

Views

Author

Ilya Gutkovskiy, Oct 02 2022

Keywords

Comments

Convolution inverse of A067593.

Crossrefs

Cf. A000032, A067593, A093996, A357380, A357382.

Programs

  • Mathematica
    nmax = 100; CoefficientList[Series[Product[(1 - x^LucasL[k]), {k, 0, 20}], {x, 0, nmax}], x]
Showing 1-4 of 4 results.

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

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