A288005 Number of symmetrical fountains of n coins.

1, 1, 1, 2, 1, 3, 3, 5, 4, 9, 8, 15, 14, 26, 24, 46, 42, 79, 73, 137, 128, 239, 221, 414, 385, 719, 668, 1249, 1161, 2167, 2016, 3762, 3499, 6531, 6075, 11336, 10546, 19676, 18306, 34153, 31775, 59279, 55155, 102890, 95733, 178587, 166165, 309968, 288412

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..8354

Example

a(7) = 5:
.. O O O ....... O O ....... O ... O ......... O ........................
. O O O O ... O O O O O ... O O O O O ... O O O O O O ... O O O O O O O .

Maple

b:= proc(n, i, p) option remember; `if`(n<0, 0, `if`(n=0,
      `if`(p<0 and i=1, 1, 0), `if`(n=i or n=i+p, 1, 0)+
      `if`(i<1 and p=1, 0, b(n-2*i, i, -p))+b(n-2*(i+p), i+p, -p)))
    end:
a:= n-> `if`(n=0, 1, b(n, 0, 1)):
seq(a(n), n=0..60);  # Alois P. Heinz, Sep 02 2017

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n < 0, 0, If[n == 0, If[p < 0 && i == 1, 1, 0], If[n == i || n == i + p, 1, 0] + If[i < 1 && p == 1, 0, b[n - 2i, i, -p]] + b[n - 2(i + p), i + p, -p]]];
a[n_] := If[n == 0, 1, b[n, 0, 1]];
a /@ Range[0, 60] (* Jean-François Alcover, Nov 14 2020, after Alois P. Heinz *)

Crossrefs

Cf. A005169, A288006.

Sequence in context: A343379 A026927 A240863 * A237832 A074500 A107237

Adjacent sequences: A288002 A288003 A288004 * A288006 A288007 A288008

Keyword

nonn

Author

Seiichi Manyama, Sep 01 2017

Extensions

a(33)-a(48) from Alois P. Heinz, Sep 02 2017

Status

approved