A060820 (2*n-1)^2 + (2*n)^2.

5, 25, 61, 113, 181, 265, 365, 481, 613, 761, 925, 1105, 1301, 1513, 1741, 1985, 2245, 2521, 2813, 3121, 3445, 3785, 4141, 4513, 4901, 5305, 5725, 6161, 6613, 7081, 7565, 8065, 8581, 9113, 9661, 10225, 10805, 11401, 12013, 12641, 13285, 13945, 14621, 15313

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

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: x*(5+10*x+x^2)/(1-x)^3. - Colin Barker, Apr 22 2012

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) for (n=1, 1000, write("b060820.txt", n, " ", (2*n - 1)^2 + (2*n)^2); ) \\ Harry J. Smith, Jul 12 2009

Crossrefs

Sequence in context: A228169 A152734 A080856 * A182211 A146404 A323187

Adjacent sequences: A060817 A060818 A060819 * A060821 A060822 A060823

Keyword

easy,nonn

Author

Jason Earls, May 05 2001

Status

approved