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.

A331922 Number of compositions (ordered partitions) of n into distinct Lucas numbers (beginning with 1).

Original entry on oeis.org

1, 1, 0, 1, 3, 2, 0, 3, 8, 0, 2, 9, 8, 0, 8, 32, 6, 0, 9, 32, 0, 8, 38, 30, 0, 32, 150, 0, 6, 33, 32, 0, 32, 158, 30, 0, 38, 174, 0, 30, 176, 150, 0, 150, 870, 24, 0, 33, 152, 0, 32, 182, 150, 0, 158, 894, 0, 30, 182, 174, 0, 174, 1014, 144, 0, 176, 990, 0, 150, 1014, 864
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 01 2020

Keywords

Examples

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

Links

Crossrefs

Cf. A000204, A003263, A054770 (positions of 0's), A067592, A067595, A218396, A288039.

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.

A357384 Expansion of 1 / (1 + Sum_{k>=1}(-x)^Lucas(k)).

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 3, 4, 5, 7, 10, 14, 19, 26, 36, 48, 64, 87, 116, 155, 210, 283, 382, 518, 701, 948, 1282, 1732, 2339, 3158, 4263, 5756, 7772, 10495, 14176, 19148, 25865, 34941, 47198, 63753, 86114, 116311, 157095, 212181, 286580, 387070, 522805, 706142, 953777, 1288260, 1740044
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 26 2022

Keywords

Crossrefs

Cf. A000204, A080889, A288039.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[1/(1 + Sum[(-x)^LucasL[k], {k, 1, 20}]), {x, 0, nmax}], x]

A378698 Number of compositions of n into parts whose sizes are Fibonacci or Lucas numbers.

Original entry on oeis.org

1, 1, 2, 4, 8, 16, 31, 62, 123, 243, 481, 953, 1887, 3737, 7399, 14652, 29014, 57452, 113767, 225279, 446095, 883352, 1749201, 3463746, 6858864, 13581833, 26894570, 53256275, 105457382, 208825335, 413513204, 818833458, 1621443338, 3210760963, 6357907009
Offset: 0

Views

Author

Davide Rotondo, Dec 04 2024

Keywords

Comments

a(n+1)/a(n) approximate the constant r = 1.9801869...

Crossrefs

Cf. A000032, A000045, A116470.
Cf. A076739, A288039.

Programs

  • PARI
    A116470(n) = if(n<6, n, if(n%2, fibonacci(n\2+3), fibonacci(n\2)+fibonacci(n\2+2)))
a(max_n) = {Vec(1/(1+sum(k=1,max_n-1, -1*x^A116470(k)))+O(x^max_n)); } \\ Thomas Scheuerle, Dec 04 2024

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A116470(k)). - Thomas Scheuerle, Dec 04 2024
Showing 1-4 of 4 results.

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

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