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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 02:19 EDT 2021. Contains 347577 sequences. (Running on oeis4.)