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)
Sum_{n>=1} 1/a(n) = 3*log(3)/2 - (1/sqrt(3)+1/4)*Pi - sqrt(3)*log(2-sqrt(3))/2. - Amiram Eldar, Jan 13 2024
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Patrick De Geest
STATUS
approved