A214254 Number of compositions of n where differences between neighboring parts are in {-2,2}.

1, 1, 1, 1, 3, 2, 3, 2, 6, 4, 4, 3, 13, 6, 5, 6, 21, 10, 10, 9, 33, 18, 14, 15, 58, 30, 19, 27, 96, 51, 31, 44, 159, 89, 45, 77, 271, 152, 66, 133, 456, 263, 104, 228, 768, 458, 156, 395, 1310, 791, 236, 685, 2228, 1371, 363, 1187, 3802, 2380, 551, 2056, 6509

Offset: 0

Author

Alois P. Heinz, Jul 08 2012

Keywords

• nonn

Examples

			a(7) = 2: [7], [3,1,3].
a(8) = 6: [8], [5,3], [3,5], [3,1,3,1], [2,4,2], [1,3,1,3].
a(9) = 4: [9], [5,3,1], [1,3,5], [1,3,1,3,1].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..5000

Crossrefs

Column k=2 of A214247.

Programs

Maple

b:= proc(n, i) option remember;
      `if`(n<1 or i<1, 0, `if`(n=i, 1, add(b(n-i, i+j), j=[-2, 2])))
    end:
a:= n-> `if`(n=0, 1, add(b(n, j), j=1..n)):
seq(a(n), n=0..80);

Mathematica

b[n_, i_] := b[n, i] = If[n < 1 || i < 1, 0, If[n == i, 1, Sum[b[n-i, i+j], { j, {-2, 2}}]]]; a[n_] := If[n == 0, 1, Sum[b[n, j], {j, 1, n}]]; Table [a[n], {n, 0, 80}] // Flatten (* Jean-François Alcover, Dec 13 2013, translated from Maple *)