|
| |
|
|
A001080
|
|
a(n) = 16*a(n-1)-a(n-2) with a(0) = 0, a(1) = 3.
(Formerly M3155 N1278)
|
|
5
| |
|
|
0, 3, 48, 765, 12192, 194307, 3096720, 49353213, 786554688, 12535521795, 199781794032, 3183973182717, 50743789129440, 808716652888323, 12888722657083728, 205410845860451325, 3273684811110137472, 52173546131901748227, 831503053299317834160
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Also 7*x^2+1 is a square. n=7 in PARI script below. - Cino Hilliard (hillcino368(AT)gmail.com), Mar 08 2003
|
|
|
REFERENCES
| H. Brocard, Notes e'le'mentaires sur le proble`me de Peel, Nouvelles Correspondance Math\'{e}matique, 4 (1878), 161-169.
M. Davis, One equation to rule them all, Trans. New York Acad. Sci. Ser. II, 30 (1968), 766-773, http://www.rand.org/pubs/research_memoranda/RM5494.html
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
V. Th\'{e}bault, Les R\'{e}cr\'{e}ations Math\'{e}matiques. Gauthier-Villars, Paris, 1952, p. 281.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to linear recurrences with constant coefficients
|
|
|
FORMULA
| G.f.: 3x/(1-16x+x^2).
a(n) = 15*(a(n-1)+a(n-2))-a(n-3). a(n) = 17*(a(n-1)-a(n-2))+a(n-3). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 20 2006
a(n)=(1/14)*sqrt(7)*[8+3*sqrt(7)]^n-(1/14)*[8-3*sqrt(7)]^n*sqrt(7), with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Oct 02 2008]
a(n) = 16*a(n-1) - a(n-2) with a(1)=0 and a(2)=3. - Sture Sjöstedt, Nov 18 2011
|
|
|
MAPLE
| A001080:=3*z/(1-16*z+z**2); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]
|
|
|
MATHEMATICA
| LinearRecurrence[{16, -1}, {0, 3}, 30] (* From Harvey P. Dale, Nov 01 2011 *)
|
|
|
PROG
| (PARI) nxsqp1(m, n) = { for(x=1, m, y = n*x*x+1; if(issquare(y), print1(x" ")) ) }
|
|
|
CROSSREFS
| Equals 3 * A077412. Bisection of A084069. Cf. A048907.
Cf. A001081, A010727 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 16 2009]
Sequence in context: A081540 A024042 A007654 * A099852 A195635 A203427
Adjacent sequences: A001077 A001078 A001079 * A001081 A001082 A001083
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000
|
| |
|
|
