OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
W. Sierpiński, Sur les nombres pentagonaux, Bull. Soc. Roy. Sci. Liège 33 (1964) 513-517.
W. Sierpiński, Sur les nombres pentagonaux, Bull. Soc. Roy. Sci. Liège 33 (1964) 513-517.
Eric Weisstein's World of Mathematics, Pentagonal Triangular Number.
Index entries for linear recurrences with constant coefficients, signature (15,-15,1)
FORMULA
From Warut Roonguthai, Jan 05 2001: (Start)
a(n) = 14*a(n-1) - a(n-2) - 2.
G.f.: x*(1-3*x)/((1-x)*(1-14*x+x^2)). (End)
a(n+1) = 7*a(n) - 1 + 2*sqrt(12*a(n)^2 - 4*a(n) + 1). - Richard Choulet, Sep 19 2007
a(n+1) = 15*a(n) - 15*a(n-1) + a(n-2), a(1)=1, a(2)=12, a(3)=165. - Sture Sjöstedt, May 29 2009
a(n) = (1/12)*(2 - (7 - 4*sqrt(3))^n*(1 + sqrt(3)) + (-1 + sqrt(3))*(7 + 4*sqrt(3))^n). - Alan Michael Gómez Calderón, Jun 30 2024
MATHEMATICA
LinearRecurrence[{15, -15, 1}, {0, 1, 12}, 20] (* Harvey P. Dale, Aug 22 2011 *)
PROG
(Magma) [ n eq 1 select 0 else n eq 2 select 1 else 14*Self(n-1)-Self(n-2)-2: n in [1..20] ]; // Vincenzo Librandi, Aug 23 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved