|
|
A017173
|
|
a(n) = 9*n + 1.
|
|
43
|
|
|
1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 199, 208, 217, 226, 235, 244, 253, 262, 271, 280, 289, 298, 307, 316, 325, 334, 343, 352, 361, 370, 379, 388, 397, 406, 415, 424, 433, 442, 451, 460, 469, 478
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
If A=[A147296] 9*n^2+2*n (n>0, 11, 40, 87, ...); Y=[A010701] 3 (3, 3, 3, ...); X=[A017173] 9*n+1 (n>0, 10, 19, 28, ...), we have, for all terms, Pell's equation X^2 - A*Y^2 = 1. Example: 10^2 - 11*3^2 = 1; 19^2 - 40*3^2 = 1; 28^2 - 87*3^2 = 1. - Vincenzo Librandi, Aug 01 2010
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1 + 8*x)/(1 - x)^2.
|
|
MATHEMATICA
|
LinearRecurrence[{2, -1}, {1, 10}, 60] (* Harvey P. Dale, Dec 27 2014 *)
|
|
PROG
|
(Sage) [i+1 for i in range(480) if gcd(i, 9) == 9] # Zerinvary Lajos, May 20 2009
(Haskell)
a017173 = (+ 1) . (* 9)
|
|
CROSSREFS
|
Cf. A093644 ((9, 1) Pascal, column m=1).
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|