A195028 a(n) = n*(14*n + 13).

0, 27, 82, 165, 276, 415, 582, 777, 1000, 1251, 1530, 1837, 2172, 2535, 2926, 3345, 3792, 4267, 4770, 5301, 5860, 6447, 7062, 7705, 8376, 9075, 9802, 10557, 11340, 12151, 12990, 13857, 14752, 15675, 16626, 17605, 18612, 19647, 20710, 21801, 22920, 24067, 25242

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, 27, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Numbers opposite to the semi-diagonal A195024 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, A185019, A193053, A195019, A195020, A195021, A195023, A195024, A195025, A195026, A195027, A195320, A198017.

Programs

Magma

[14*n^2 +13*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011

PARI

a(n)=n*(14*n+13) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 14*n^2 + 13*n.

G.f.: x*(27+x)/(1-x)^3. - Colin Barker, Jan 09 2012

From Elmo R. Oliveira, Dec 30 2024: (Start)

E.g.f.: exp(x)*x*(27 + 14*x).

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

Extensions

Name suggested by Bruno Berselli, Oct 13 2011