A195027 a(n) = 2*n*(7*n + 5).

0, 24, 76, 156, 264, 400, 564, 756, 976, 1224, 1500, 1804, 2136, 2496, 2884, 3300, 3744, 4216, 4716, 5244, 5800, 6384, 6996, 7636, 8304, 9000, 9724, 10476, 11256, 12064, 12900, 13764, 14656, 15576, 16524, 17500, 18504, 19536, 20596, 21684, 22800, 23944, 25116, 26316

Offset: 0

Author

Omar E. Pol, Oct 13 2011

Keywords

• nonn
• easy

Comments

Sequence found by reading the line from 0, in the direction 0, 24, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Semi-axis opposite to A195023 in the same square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A144555, A152760, A179986, A195019, A195020, A195021, A195023, A195024, A195025, A195026, A195320.

Cf. A185019, A193053, A198017.

Programs

Magma

[14*n^2 +10*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011

Mathematica

Table[2n(7n+5),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,24,76},50] (* Harvey P. Dale, Jul 24 2012 *)

PARI

a(n)=2*n*(7*n+5) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 14*n^2 + 10*n.

a(n) = 4*A179986(n). - Bruno Berselli, Oct 13 2011

G.f.: 4*x*(6+x)/(1-x)^3. - Colin Barker, Jan 09 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=0, a(1)=24, a(2)=76. - Harvey P. Dale, Jul 24 2012

E.g.f.: 2*exp(x)*x*(12 + 7*x). - Elmo R. Oliveira, Dec 30 2024