A111648 a(n) = A001541(n)^2 + A001653(n+1)^2 + A002315(n)^2.

3, 83, 2811, 95483, 3243603, 110187011, 3743114763, 127155714923, 4319551192611, 146737584833843, 4984758333158043, 169335045742539611, 5752406796913188723, 195412496049305876963

Offset: 0

Author

Charlie Marion, Aug 24 2005

Keywords

• nonn
• easy

Examples

			a(1) = 83 = 3^2+5^2+7^2.
		

Links

• Ray Chandler, Table of n, a(n) for n = 0..652
• Index entries for linear recurrences with constant coefficients, signature (35,-35,1).

Crossrefs

Cf. A001541, A001653, A002315, A111647, A111649.

Programs

Mathematica

LinearRecurrence[{35, -35, 1}, {3, 83, 2811}, 20] (* Paolo Xausa, Feb 06 2024 *)

Formula

a(n) = A038761(n)^2 + 2, e.g., 95483 = 309^2 + 2.

a(n) = A001652(2*n+1) - A001109(n+1)^2 - Sum_{k=1..n-1} A038723(2*n), e.g., 95483 = 137903 - 204^2 - (23 + 781).

For n > 0, 2*a(n) + A001652(2*n-1) = A001653(2*n+2), e.g., 2*2811 + 119 = 5741.

G.f.: -(11*x^2-22*x+3) / ((x-1)*(x^2-34*x+1)). - Colin Barker, Dec 14 2014 (Empirical g.f. confirmed for more terms and recurrence of source sequences. - Ray Chandler, Feb 05 2024)