|
|
A033571
|
|
a(n) = (2*n + 1)*(5*n + 1).
|
|
10
|
|
|
1, 18, 55, 112, 189, 286, 403, 540, 697, 874, 1071, 1288, 1525, 1782, 2059, 2356, 2673, 3010, 3367, 3744, 4141, 4558, 4995, 5452, 5929, 6426, 6943, 7480, 8037, 8614, 9211, 9828, 10465, 11122, 11799, 12496, 13213, 13950, 14707, 15484, 16281, 17098, 17935, 18792, 19669, 20566, 21483
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Sequence found by reading the line from 1, in the direction 1, 18, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. This is one of the diagonals in the spiral. - Omar E. Pol, Sep 10 2011
Also sequence found by reading the line from 1, in the direction 1, 18, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. This is a line perpendicular to the main axis A195015 in the same spiral. - Omar E. Pol, Oct 14 2011
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1 + 15*x + 4*x^2)/(1-x)^3.
E.g.f.: (1 + 17*x + 10*x^2)*exp(x). (End)
Sum_{n>=0} 1/a(n) = sqrt(1+2/sqrt(5))*Pi/6 + sqrt(5)*log(phi)/6 + 5*log(5)/12 - 2*log(2)/3, where phi is the golden ratio (A001622). - Amiram Eldar, Aug 23 2022
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[(2*n+1)*(5*n+1), {n, 0, 50}] (* G. C. Greubel, Oct 12 2019 *)
|
|
PROG
|
(Magma) [(2*n+1)*(5*n+1): n in [0..50]] # G. C. Greubel, Oct 12 2019
(Sage) [(2*n+1)*(5*n+1) for n in range(50)] # G. C. Greubel, Oct 12 2019
(GAP) List([0..50], n-> (2*n+1)*(5*n+1)); # G. C. Greubel, Oct 12 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|