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A162395 a(n) = -(-1)^n * n^2. 6
1, -4, 9, -16, 25, -36, 49, -64, 81, -100, 121, -144, 169, -196, 225, -256, 289, -324, 361, -400, 441, -484, 529, -576, 625, -676, 729, -784, 841, -900, 961, -1024, 1089, -1156, 1225, -1296, 1369, -1444, 1521, -1600, 1681, -1764, 1849, -1936, 2025, -2116, 2209, -2304, 2401, -2500 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is the denominator of ((pi)^2)/12 = 1/1-1/4+1/9-1/16+1/25-1/36+... - Mohammad K. Azarian, Dec 29 2011

Also, circulant determinant of [1,2,...,n,n-1,...,1], i.e., determinant of the (2n-1) X (2n-1) matrix which has this as first row (and also first column), where row k+1 is obtained by cyclically shifting row k one place to the left. - M. F. Hasler, Dec 17 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

M. Somos, Rational Function Multiplicative Coefficients

Index entries for linear recurrences with constant coefficients, signature (-3,-3,-1).

FORMULA

Euler transform of length 2 sequence [ -4, 3].

a(n) is multiplicative with a(2^e) = -(4^e) if e>0, a(p^e) = (p^2)^e if p>2.

G.f.: x * (1 - x) / (1 + x)^3.

E.g.f.: exp(-x) * (x - x^2).

a(n) = a(-n) = -(-1)^n * A000290(n) for all n in Z.

EXAMPLE

G.f. = x - 4*x^2 + 9*x^3 - 16*x^4 + 25*x^5 - 36*x^6 + 49*x^7 - 64*x^8 + 81*x^9 + ...

MATHEMATICA

Table[(-1)^(n+1) * n^2, {n, 60}] (* Vincenzo Librandi, Feb 15 2013 *)

PROG

(PARI) {a(n) = -(-1)^n * n^2};

(MAGMA) [(-1)^(n+1) * n^2: n in [1..60]]; // Vincenzo Librandi, Feb 15 2013

CROSSREFS

Cf. A000290.

For the reversion of this sequence see A263843 (and also A007297).

Sequence in context: A174902 A000290 * A253909 A221222 A144913 A018885

Adjacent sequences:  A162392 A162393 A162394 * A162396 A162397 A162398

KEYWORD

sign,mult,easy

AUTHOR

Michael Somos, Jul 02 2009

STATUS

approved

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Last modified December 12 20:04 EST 2017. Contains 295954 sequences.