A195030 a(n) = (n-2)*(14*n-39) for n > 2, otherwise a(n) = n.

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

Author

Omar E. Pol, Oct 18 2011

Keywords

• nonn
• easy

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].

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).

Crossrefs

Cf. A195019, A195020, A195021, A185019, A193053, A198017.

Programs

Magma

[0,1,2] cat[(n-2)*(14*n-39): n in [3..50]]; // Vincenzo Librandi, Jul 10 2012

Mathematica

Join[{0,1,2},Table[(n-2)*(14*n-39),{n,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

Formula

G.f.: x*(1-x+30*x^3-2*x^4)/(1-x)^3. - Bruno Berselli, Oct 18 2011

Extensions

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