OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1750
FORMULA
a(n) ~ c * d^n, where d = 1.55950091106966174000570854045613844480247532446123619115121795622156266..., c = 0.42021981384104890468461570042297109905705539874851026797544718780579866... - Vaclav Kotesovec, Feb 28 2020
EXAMPLE
a(4) = 3: 13, 31, 4.
a(5) = 4: 131, 14, 41, 5.
a(6) = 6: 141, 24, 42, 15, 51, 6.
a(7) = 9: 313, 142, 241, 151, 25, 52, 16, 61, 7.
a(8) = 15: 1313, 3131, 242, 314, 413, 152, 251, 35, 53, 161, 26, 62, 17, 71, 8.
a(9) = 23: 13131, 1314, 1413, 3141, 4131, 414, 252, 135, 153, 315, 351, 513, 531, 162, 261, 36, 63, 171, 27, 72, 18, 81, 9.
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, add(`if`(abs
(i-j)<2, 0, b(n-j, `if`(n<2*j-1, -1, j))), j=1..n))
end:
a:= n-> b(n, -1):
seq(a(n), n=0..50);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[If[Abs[i - j] < 2, 0,
b[n - j, If[n < 2*j - 1, -1, j]]], {j, 1, n}]];
a[n_] := b[n, -1];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Apr 13 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 25 2020
STATUS
approved