

A301503


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


1



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
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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 * A059431 A289358 A271698
Adjacent sequences: A301500 A301501 A301502 * A301504 A301505 A301506


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Mar 22 2018


STATUS

approved



