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A195030
a(n) = (n-2)*(14*n-39) 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
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 semi-axis of the square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].
FORMULA
G.f.: x*(1-x+30*x^3-2*x^4)/(1-x)^3. - Bruno Berselli, Oct 18 2011
MATHEMATICA
Join[{0, 1, 2}, Table[(n-2)*(14*n-39), {n, 3, 50}]] (* Vincenzo Librandi, Jul 10 2012 *)
PROG
(Magma) [0, 1, 2] cat[(n-2)*(14*n-39): 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
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