

A162395


a(n) = (1)^n * n^2.


7



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
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OFFSET

1,2


COMMENTS

This sequence is the denominator of ((pi)^2)/12 = 1/11/4+1/91/16+1/251/36+...  Mohammad K. Azarian, Dec 29 2011
Also, circulant determinant of [1,2,...,n,n1,...,1], i.e., determinant of the (2n1) X (2n1) 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: A000290 * A253909 A305559 A221222 A144913 A018885
Adjacent sequences: A162392 A162393 A162394 * A162396 A162397 A162398


KEYWORD

sign,mult,easy


AUTHOR

Michael Somos, Jul 02 2009


STATUS

approved



