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A087420 a(n) is the sum of the squares of the sizes of the conjugacy classes in the dihedral group D_2n. 1
2, 4, 14, 14, 34, 28, 62, 46, 98, 68, 142, 94, 194, 124, 254, 158, 322, 196, 398, 238, 482, 284, 574, 334, 674, 388, 782, 446, 898, 508, 1022, 574, 1154, 644, 1294, 718, 1442, 796, 1598, 878, 1762, 964, 1934, 1054, 2114, 1148, 2302, 1246, 2498, 1348, 2702 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

FORMULA

For even n, a(n) = n^2/2 + 2n - 2. For odd n, a(n) = n^2 + 2n - 1. - Eric M. Schmidt, Apr 20 2013

From Colin Barker, Feb 24 2017: (Start)

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>6.

G.f.: 2*x*(1 + 2*x + 4*x^2 + x^3 - x^4 - x^5) / ((1 - x)^3*(1 + x)^3).

(End)

PROG

(Sage) def A087420(n) : return n^2//2 + 2*n - 2 if is_even(n) else n^2 + 2*n - 1 # Eric M. Schmidt, Apr 20 2013

(PARI) Vec(2*x*(1 + 2*x + 4*x^2 + x^3 - x^4 - x^5) / ((1 - x)^3*(1 + x)^3) + O(x^70)) \\ Colin Barker, Feb 24 2017

CROSSREFS

Sequence in context: A131758 A095909 A151872 * A194388 A141654 A173338

Adjacent sequences:  A087417 A087418 A087419 * A087421 A087422 A087423

KEYWORD

nonn,easy

AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 22 2003

EXTENSIONS

More terms from Eric M. Schmidt, Apr 20 2013

STATUS

approved

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Last modified October 16 02:45 EDT 2018. Contains 316252 sequences. (Running on oeis4.)