A087348 a(n) = 10*n^2 - 6*n + 1.

5, 29, 73, 137, 221, 325, 449, 593, 757, 941, 1145, 1369, 1613, 1877, 2161, 2465, 2789, 3133, 3497, 3881, 4285, 4709, 5153, 5617, 6101, 6605, 7129, 7673, 8237, 8821, 9425, 10049, 10693, 11357, 12041, 12745, 13469, 14213, 14977, 15761, 16565, 17389, 18233, 19097

Offset: 1

Author

Charlie Marion, Oct 20 2003

Keywords

• nonn
• easy

Comments

Sequence found by reading the line from 5, in the direction 5, 29, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Jul 18 2012

Examples

			a(3)=73 since 73^2 = 48^2 + 55^2 = (4*12)^2 + (48 + 7)^2. See 1st formula.
		

Links

• Shawn A. Broyles, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000326, A033567, A033579, A056220, A085787, A153784.

Programs

Mathematica

Table[10*n^2 - 6*n + 1, {n, 50}] (* Paolo Xausa, Jul 18 2024 *)

PARI

a(n)=10*n^2-6*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n)^2 = A033579(n)^2 + A033567(n)^2 = (4*A000326(n))^2 + (A033579(n) + A056220(n-1))^2.

From Colin Barker, Jun 30 2012: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: x*(5 + 14*x + x^2)/(1-x)^3. (End)

a(n) = 1 + A153784(n). - Omar E. Pol, Jul 18 2012

E.g.f.: exp(x)*(10*x^2 + 4*x + 1) - 1. - Elmo R. Oliveira, Oct 31 2024

Extensions

More terms from Ray Chandler, Oct 22 2003