OFFSET
1,1
REFERENCES
Marilyn vos Savant and Leonore Fleischer, Brain Building in Just 12 Weeks, Bantam Books, New York, NY, 1991, pp. 104-105, 119.
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Colin Barker, Apr 22 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(5+10*x+x^2)/(1-x)^3. (End)
E.g.f.: exp(x)*(8*x^2 + 4*x + 1) - 1. - Elmo R. Oliveira, Nov 17 2025
EXAMPLE
a(1)=5 because 1^2+2^2=5.
a(2)=25 because 3^2+4^2=25.
MATHEMATICA
Table[(2*n - 1)^2 + (2*n)^2, {n, 300}] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2012 *)
LinearRecurrence[{3, -3, 1}, {5, 25, 61}, 60] (* Harvey P. Dale, Oct 13 2020 *)
PROG
(PARI) a(n) = (2*n - 1)^2 + (2*n)^2 \\ Harry J. Smith, Jul 12 2009
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason Earls, May 05 2001
STATUS
approved