

A195021


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


9



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
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OFFSET

0,2


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).


FORMULA

a(n) = 14*n^2  11*n.
From Colin Barker, Apr 09 2012: (Start)
a(n) = 3*a(n1)  3*a(n2) + a(n3).
G.f.: x*(3+25*x)/(1x)^3. (End)


PROG

(MAGMA) [14*n^2  11*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011
(PARI) a(n)=n*(14*n11) \\ Charles R Greathouse IV, Oct 07 2015


CROSSREFS

Cf. A144555, A152760, A185019, A193053, A195019, A195020, A195023, A195024, A195025, A195030, A195320, A198017.
Cf. numbers of the form n*(n*kk+6))/2, this sequence is the case k=28: see Comments lines of A226492.
Sequence in context: A003348 A344641 A086488 * A344429 A274871 A042041
Adjacent sequences: A195018 A195019 A195020 * A195022 A195023 A195024


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Sep 07 2011


EXTENSIONS

Edited by Bruno Berselli, Oct 18 2011


STATUS

approved



