0,2

Sequence found by reading the line from 0, in the direction 0, 21, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Semi-diagonal opposite to A195320 in the same square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].

Sum of the numbers from 6*n to 8*n. - Wesley Ivan Hurt, Dec 23 2015

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

a(n) = 14*n^2 + 7*n.

a(n) = 7*A014105(n). - Bruno Berselli, Oct 13 2011

From Colin Barker, Apr 09 2012: (Start)

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

G.f.: 7*x*(3+x)/(1-x)^3. (End)

a(n) = Sum_{i=6*n..8*n} i. - Wesley Ivan Hurt, Dec 23 2015

E.g.f.: 7*exp(x)*x*(3 + 2*x). - Elmo R. Oliveira, Dec 29 2024

A195026:=n->7*n*(2*n+1): seq(A195026(n), n=0..50); # Wesley Ivan Hurt, Dec 23 2015

Table[7*n*(2*n + 1), {n, 0, 50}] (* Wesley Ivan Hurt, Dec 23 2015 *)

LinearRecurrence[{3, -3, 1}, {0, 21, 70}, 50] (* Harvey P. Dale, Apr 26 2017 *)

(Magma) [14*n^2 +7*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011

(PARI) a(n)=7*n*(2*n+1) \\ Charles R Greathouse IV, Jun 17 2017

Cf. A014105, A144555, A152760, A195019, A195020, A195021, A195023, A195024, A195025, A195320.

Cf. A185019, A193053, A198017.

Sequence in context: A200931 A044159 A044540 * A296035 A102233 A309903

Adjacent sequences: A195023 A195024 A195025 * A195027 A195028 A195029

nonn,easy

Omar E. Pol, Oct 13 2011

approved