A060820 a(n) = (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

Author

Jason Earls, May 05 2001

Keywords

• easy
• nonn

Examples

			a(1)=5 because 1^2+2^2=5. a(2)=25 because 3^2+4^2=25.
		

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).

Crossrefs

Essentially identical to A080856, which is the main entry for this sequence. - N. J. A. Sloane, Jul 13 2025

Programs

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 *)

PARI

a(n) = (2*n - 1)^2 + (2*n)^2 \\ Harry J. Smith, Jul 12 2009

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