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

0,6

Links

Table of n, a(n) for n=0..61.

Index entries for sequences related to compositions

Index entries for sequences related to sums of squares

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A000290, A003242, A006456, A301502.

Sequence in context: A247310 A059220 A261630 * A378103 A378336 A059431

Adjacent sequences: A301500 A301501 A301502 * A301504 A301505 A301506

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 22 2018

Status

approved