OFFSET
0,2
COMMENTS
Sequence found by reading the segment (1, 4) together with the line (one of the diagonal axes) from 4, in the direction 4, 27, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Sep 10 2011
LINKS
FORMULA
a(n) = (2*n-1)*(5*n-1).
G.f.: (1+x+18*x^2)/(1-x)^3. - Jaume Oliver Lafont, Mar 27 2009
a(n) = a(n-1) + 20*n - 17 (with a(0)=1). - Vincenzo Librandi, Dec 03 2010
Sum_{n>=0} 1/a(n) = 1 + (2*sqrt(1+2/sqrt(5))*Pi - 2*sqrt(5)*log(phi) - 5*log(5) + 8*log(2))/12, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 22 2022
MATHEMATICA
Table[10n^2-7n+1, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 4, 27}, 50] (* Harvey P. Dale, Apr 06 2020 *)
PROG
(PARI) a(n)=10*n^2-7*n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Mar 13 2009
EXTENSIONS
Typo in definition corrected by Reinhard Zumkeller, Dec 03 2009
STATUS
approved