A195320 7 times hexagonal numbers: 7*n*(2*n-1).

0, 7, 42, 105, 196, 315, 462, 637, 840, 1071, 1330, 1617, 1932, 2275, 2646, 3045, 3472, 3927, 4410, 4921, 5460, 6027, 6622, 7245, 7896, 8575, 9282, 10017, 10780, 11571, 12390, 13237, 14112, 15015, 15946, 16905, 17892, 18907, 19950, 21021, 22120, 23247, 24402

Offset

0,2

Comments

Sequence found by reading the line from 0, in the direction 0, 7, ..., in the square spiral whose vertices are the generalized enneagonal numbers A118277.

Also sequence found by reading the same line (mentioned above) in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. This is the one of the semi-diagonals of the square spiral, which is related to the primitive Pythagorean triple [3, 4, 5]. - Omar E. Pol, Oct 13 2011

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 = 7*A000384(n).

G.f.: -7*x*(1+3*x) / (x-1)^3. - R. J. Mathar, Sep 27 2011

Prog

(Magma) [7*n*(2*n-1): n in [0..50]]; // Vincenzo Librandi, Sep 28 2011
(PARI) a(n)=7*n*(2*n-1) \\ Charles R Greathouse IV, Sep 28 2015

Crossrefs

Bisection of A024966.

Cf. A000384, A118277, A152746, A152750, A185019, A193053, A198017.

Sequence in context: A102532 A297405 A044109 * A110451 A212144 A266387

Adjacent sequences: A195317 A195318 A195319 * A195321 A195322 A195323

Keyword

nonn,easy

Author

Omar E. Pol, Sep 18 2011

Status

approved