A195021 a(n) = n*(14*n - 11).

0, 3, 34, 93, 180, 295, 438, 609, 808, 1035, 1290, 1573, 1884, 2223, 2590, 2985, 3408, 3859, 4338, 4845, 5380, 5943, 6534, 7153, 7800, 8475, 9178, 9909, 10668, 11455, 12270, 13113, 13984, 14883, 15810, 16765, 17748, 18759, 19798, 20865, 21960, 23083, 24234, 25413

Offset: 0

Author

Omar E. Pol, Sep 07 2011

Keywords

• nonn
• easy

Comments

Sequence found by reading the first two vertices [0, 3] together with the line from 34, in the direction 34, 93, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020, which is related to the primitive Pythagorean triple [3, 4, 5]. For another version see A195030.

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, A185019, A193053, A195019, A195020, A195023, A195024, A195025, A195030, A195320, A198017.

Cf. numbers of the form n*(n*k - k + 6)/2, this sequence is the case k=28: see Comments lines of A226492.

Programs

Magma

[14*n^2 - 11*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011

Mathematica

Table[n*(14*n - 11), {n, 0, 50}] (* Paolo Xausa, Jan 15 2025 *)

PARI

a(n)=n*(14*n-11) \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 14*n^2 - 11*n.

From Colin Barker, Apr 09 2012: (Start)

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

G.f.: x*(3+25*x)/(1-x)^3. (End)

E.g.f.: exp(x)*x*(3 + 14*x). - Elmo R. Oliveira, Dec 30 2024

Extensions

Edited by Bruno Berselli, Oct 18 2011