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A014633 Even pentagonal numbers. 5
0, 12, 22, 70, 92, 176, 210, 330, 376, 532, 590, 782, 852, 1080, 1162, 1426, 1520, 1820, 1926, 2262, 2380, 2752, 2882, 3290, 3432, 3876, 4030, 4510, 4676, 5192, 5370, 5922, 6112, 6700, 6902, 7526, 7740, 8400, 8626, 9322 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

FORMULA

G.f.: 2*(6+5*x+12*x^2+x^3)/((1+x)^2*(1-x)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009, corrected by R. J. Mathar, Sep 16 2009

From Ant King, Aug 16 2011: (Start)

a(n) = a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5).

a(n) = 48+2*a(n-2)-a(n-4).

a(n) = 1/8*(1-3*(-1)^(n+1)+12*(n+1))*(1-(-1)^(n+1)+4*(n+1)).(End)

MATHEMATICA

LinearRecurrence[{1, 2, -2, -1, 1}, {0, 12, 22, 70, 92}, 40] (* Harvey P. Dale, Aug 26 2014 *)

Select[PolygonalNumber[5, Range[0, 100]], EvenQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 15 2017 *)

PROG

(MAGMA) [1/8*(1-3*(-1)^(n+1)+12*(n+1))*(1-(-1)^(n+1)+4*(n+1)): n in [0..40]]; // Vincenzo Librandi, Aug 17 2011

(PARI) lista(nn) = {forstep (n=0, nn, 2, if (ispolygonal(n, 5), print1(n, ", ")); ); } \\ Michel Marcus, Jun 20 2015

CROSSREFS

Cf. A000326.

Sequence in context: A200197 A115709 A115703 * A298323 A299216 A227072

Adjacent sequences:  A014630 A014631 A014632 * A014634 A014635 A014636

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian

EXTENSIONS

More terms from Patrick De Geest

STATUS

approved

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Last modified May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)