login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A195028
a(n) = n*(14*n + 13).
2
0, 27, 82, 165, 276, 415, 582, 777, 1000, 1251, 1530, 1837, 2172, 2535, 2926, 3345, 3792, 4267, 4770, 5301, 5860, 6447, 7062, 7705, 8376, 9075, 9802, 10557, 11340, 12151, 12990, 13857, 14752, 15675, 16626, 17605, 18612, 19647, 20710, 21801, 22920
OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 27, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Numbers opposite to the semi-diagonal A195024 in the same square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].
FORMULA
a(n) = 14*n^2 + 13*n.
G.f.: x*(27+x)/(1-x)^3. - Colin Barker, Jan 09 2012
PROG
(Magma) [14*n^2 +13*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011
(PARI) a(n)=n*(14*n+13) \\ Charles R Greathouse IV, Jun 17 2017
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Oct 13 2011
EXTENSIONS
Name suggested by Bruno Berselli, Oct 13 2011
STATUS
approved