A195026 a(n) = 7*n*(2*n + 1).

0, 21, 70, 147, 252, 385, 546, 735, 952, 1197, 1470, 1771, 2100, 2457, 2842, 3255, 3696, 4165, 4662, 5187, 5740, 6321, 6930, 7567, 8232, 8925, 9646, 10395, 11172, 11977, 12810, 13671, 14560, 15477, 16422, 17395, 18396, 19425, 20482, 21567, 22680, 23821, 24990

Offset

0,2

Comments

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 6n to 8n. - Wesley Ivan Hurt, Dec 23 2015

Links

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

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

Formula

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=6n..8n} i. - Wesley Ivan Hurt, Dec 23 2015

Maple

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

Mathematica

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 *)

Prog

(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

Crossrefs

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

Keyword

nonn,easy

Author

Omar E. Pol, Oct 13 2011

Status

approved