A301503 Number of compositions (ordered partitions) of n into square parts (A000290) such that no two adjacent parts are equal (Carlitz compositions).

1, 1, 0, 0, 1, 2, 1, 0, 0, 2, 4, 2, 0, 2, 7, 8, 4, 3, 7, 14, 16, 11, 9, 18, 32, 35, 30, 32, 49, 74, 87, 83, 84, 120, 178, 209, 205, 219, 305, 434, 515, 523, 572, 785, 1080, 1255, 1303, 1488, 2002, 2644, 3058, 3284, 3849, 5077, 6518, 7525, 8319, 9927, 12803, 16051, 18623, 21081

Offset: 0

Author

Ilya Gutkovskiy, Mar 22 2018

Keywords

• nonn

Examples

			a(10) = 4 because we have [9, 1], [4, 1, 4, 1], [1, 9] and [1, 4, 1, 4].
		

Links

• Index entries for sequences related to compositions
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000290, A003242, A006456, A301502.

Programs

Mathematica

nmax = 61; CoefficientList[Series[1/(1 - Sum[x^k^2/(1 + x^k^2), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k^2)/(1 + x^(k^2))).