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

Offset

1,1

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

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).

Formula

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

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: x*(5+14*x+x^2)/(1-x)^3. - Colin Barker, Jun 30 2012

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

Example

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

Prog

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

Crossrefs

Sequence in context: A176333 A100559 A224498 * A154412 A339935 A236075

Adjacent sequences: A087345 A087346 A087347 * A087349 A087350 A087351

Keyword

nonn,easy

Author

Charlie Marion, Oct 20 2003

Extensions

More terms from Ray Chandler, Oct 22 2003

Status

approved