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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
1, 16, 57, 136, 265, 456, 721, 1072, 1521, 2080, 2761, 3576, 4537, 5656, 6945, 8416, 10081, 11952, 14041, 16360, 18921, 21736, 24817, 28176, 31825, 35776, 40041, 44632, 49561, 54840, 60481, 66496, 72897, 79696, 86905, 94536, 102601, 111112, 120081, 129520, 139441, 149856, 160777, 172216, 184185 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

R. Kemp, On the number of words in the language {w in Sigma* | w = w^R }^2, Discrete Math., 40 (1982), 225-234. See Table 1.

FORMULA

From Colin Barker, Jul 24 2013: (Start) (Conjectured formulas; later proven)

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

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

The above conjecture is true: A284873(4, n) evaluates to the same polynomial. - Andrew Howroyd, Oct 10 2017

MAPLE

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

MATHEMATICA

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

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

PROG

(PARI) a(n) = 2*n^3 + n^2 - 2*n; \\ Andrew Howroyd, Oct 10 2017

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

CROSSREFS

Row 4 of A284873.

Sequence in context: A169882 A202993 A221068 * A316443 A223313 A235679

Adjacent sequences:  A187274 A187275 A187276 * A187278 A187279 A187280

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 07 2011

STATUS

approved

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Last modified October 21 14:41 EDT 2019. Contains 328301 sequences. (Running on oeis4.)