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A187277 Let S denote the palindromes in the language {0,1,2,...,n-1}*; a(n) = number of words of length 4 in the language SS. 2

%I

%S 1,16,57,136,265,456,721,1072,1521,2080,2761,3576,4537,5656,6945,8416,

%T 10081,11952,14041,16360,18921,21736,24817,28176,31825,35776,40041,

%U 44632,49561,54840,60481,66496,72897,79696,86905,94536,102601,111112,120081,129520,139441,149856,160777,172216,184185

%N Let S denote the palindromes in the language {0,1,2,...,n-1}*; a(n) = number of words of length 4 in the language SS.

%H G. C. Greubel, <a href="/A187277/b187277.txt">Table of n, a(n) for n = 1..1000</a>

%H R. Kemp, <a href="http://dx.doi.org/10.1016/0012-365X(82)90123-6">On the number of words in the language {w in Sigma* | w = w^R }^2</a>, Discrete Math., 40 (1982), 225-234. See Table 1.

%F From _Colin Barker_, Jul 24 2013: (Start) (Conjectured formulas; later proven)

%F a(n) = n*(2*n^2 +n -2).

%F G.f.: x*(1 +12*x - x^2)/(x-1)^4. (End)

%F The above conjecture is true: A284873(4, n) evaluates to the same polynomial. - _Andrew Howroyd_, Oct 10 2017

%p Using the Maple code from A007055: [seq(F(b,4),b=1..50)];

%t Array[# (2 #^2 + # - 2) &, 45] (* or *)

%t Rest@ CoefficientList[Series[-x (x^2 - 12 x - 1)/(x - 1)^4, {x, 0, 45}], x] (* _Michael De Vlieger_, Oct 10 2017 *)

%o (PARI) a(n) = 2*n^3 + n^2 - 2*n; \\ _Andrew Howroyd_, Oct 10 2017

%o (MAGMA) [2*n^3 + n^2 - 2*n: n in [1..50]]; // _G. C. Greubel_, Jul 25 2018

%Y Row 4 of A284873.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Mar 07 2011

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Last modified November 18 02:07 EST 2019. Contains 329242 sequences. (Running on oeis4.)