

A195030


a(n) = (n2)*(14*n39) for n > 2, otherwise a(n) = n.


4



0, 1, 2, 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

0,3


COMMENTS

Union of [1, 2] and A195021.
Sequence found by reading the line from 0, in the direction 0, 1,..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. This is the one of the semiaxis of the square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Bruno Berselli, Illustration of initial terms: An origin of A195030
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: x*(1x+30*x^32*x^4)/(1x)^3.  Bruno Berselli, Oct 18 2011


MATHEMATICA

Join[{0, 1, 2}, Table[(n2)*(14*n39), {n, 3, 50}]] (* Vincenzo Librandi, Jul 10 2012


PROG

(MAGMA) [0, 1, 2] cat[(n2)*(14*n39): n in [3..50]]; // Vincenzo Librandi, Jul 10 2012
(PARI) a(n)=if(n, ([0, 1, 0; 0, 0, 1; 1, 3, 3]^n*[0; 1; 2])[1, 1], 0) \\ Charles R Greathouse IV, Oct 16 2015


CROSSREFS

Cf. A195019, A195020, A195021, A185019, A193053, A198017.
Sequence in context: A073657 A228114 A025136 * A092981 A042167 A126910
Adjacent sequences: A195027 A195028 A195029 * A195031 A195032 A195033


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Oct 18 2011


EXTENSIONS

Both sequence (based on A195021) and definition suggested by Bruno Berselli, Oct 18 2011


STATUS

approved



