|
| |
|
|
A157262
|
|
36n^2 - 55n + 21.
|
|
3
| |
|
|
2, 55, 180, 377, 646, 987, 1400, 1885, 2442, 3071, 3772, 4545, 5390, 6307, 7296, 8357, 9490, 10695, 11972, 13321, 14742, 16235, 17800, 19437, 21146, 22927, 24780, 26705, 28702, 30771, 32912, 35125, 37410, 39767, 42196, 44697, 47270
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The identity (10368*n^2-15840*n+6049)^2-(36*n^2-55*n+21)*(1728*n-1320)^2=1 can be written as A157264(n)^2-a(n)*A157263(n)^2=1. - Vincenzo Librandi, Jan 27 2012
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
| a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jan 27 2012
G.f.: x*(-2-49*x-21*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 27 2012
a(n) = A016813(n-1)*A017185(n-1). - Bruno Berselli, Jan 27 2012
|
|
|
MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {2, 55, 180}, 40] (* Vincenzo Librandi, Jan 27 2012 *)
|
|
|
PROG
| (PARI) a(n)=36*n^2-55*n+21 \\ Charles R Greathouse IV, Dec 28 2011
(MAGMA) I:=[2, 55, 180]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 27 2012
|
|
|
CROSSREFS
| Cf. A157263, A157264.
Sequence in context: A117681 A089180 A034013 * A007975 A109796 A186886
Adjacent sequences: A157259 A157260 A157261 * A157263 A157264 A157265
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 26 2009
|
| |
|
|
