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A195027 a(n) = 2*n*(7*n + 5). 3
0, 24, 76, 156, 264, 400, 564, 756, 976, 1224, 1500, 1804, 2136, 2496, 2884, 3300, 3744, 4216, 4716, 5244, 5800, 6384, 6996, 7636, 8304, 9000, 9724, 10476, 11256, 12064, 12900, 13764, 14656, 15576, 16524, 17500, 18504, 19536, 20596, 21684, 22800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequence found by reading the line from 0, in the direction 0, 24, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Semi-axis opposite to A195023 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).

FORMULA

a(n) = 14*n^2 + 10*n.

a(n) = 4*A179986(n). - Bruno Berselli, Oct 13 2011

G.f.: 4*x*(6+x)/(1-x)^3. - Colin Barker, Jan 09 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=0, a(1)=24, a(2)=76. - Harvey P. Dale, Jul 24 2012

MATHEMATICA

Table[2n(7n+5), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 24, 76}, 50] (* Harvey P. Dale, Jul 24 2012 *)

PROG

(MAGMA) [14*n^2 +10*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011

(PARI) a(n)=2*n*(7*n+5) \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A144555, A152760, A179986, A195019, A195020, A195021, A195023, A195024, A195025, A195026, A195320.

Cf. A185019, A193053, A198017.

Sequence in context: A033572 A233883 A291630 * A325958 A211574 A211588

Adjacent sequences:  A195024 A195025 A195026 * A195028 A195029 A195030

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Oct 13 2011

STATUS

approved

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Last modified July 31 04:19 EDT 2021. Contains 346367 sequences. (Running on oeis4.)