|
|
A017330
|
|
a(n) = (10*n + 5)^2.
|
|
5
|
|
|
25, 225, 625, 1225, 2025, 3025, 4225, 5625, 7225, 9025, 11025, 13225, 15625, 18225, 21025, 24025, 27225, 30625, 34225, 38025, 42025, 46225, 50625, 55225, 60025, 65025, 70225, 75625, 81225, 87025, 93025, 99225, 105625, 112225, 119025, 126025, 133225, 140625
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
This is an old school trick which says that a square of an integer that ends with 5 is easy to compute. Remove the 5, multiply the remaining number by (itself + 1), and concatenate 25 at the end. So, a(n)\100 = A002378(n). - Michel Marcus, Dec 23 2013
|
|
LINKS
|
|
|
FORMULA
|
G.f.: -25*(x^2 + 6*x + 1)/(x - 1)^3. - Colin Barker, Nov 14 2012
Sum_{n>=0} 1/a(n) = Pi^2/200.
Sum_{n>=0} (-1)^n/a(n) = G/25, where G is Catalan's constant (A006752). (End)
|
|
EXAMPLE
|
5^2 = 25;
15^2 = (1 * 2) concatenate 25 = 225;
25^2 = (2 * 3) concatenate 25 = 625;
35^2 = (3 * 4) concatenate 25 = 1225;
45^2 = (4 * 5) concatenate 25 = 2025;
55^2 = (5 * 6) concatenate 25 = 3025;
65^2 = (6 * 7) concatenate 25 = 4225, etc.
|
|
MATHEMATICA
|
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|