|
| |
|
|
A038723
|
|
a(n)=6a(n-1)-a(n-2), n >= 2, a(0)=1, a(1)=4.
|
|
6
| |
|
|
1, 4, 23, 134, 781, 4552, 26531, 154634, 901273, 5253004, 30616751, 178447502, 1040068261, 6061962064, 35331704123, 205928262674, 1200237871921, 6995498968852, 40772755941191, 237641036678294, 1385073464128573
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7 (1969), pp. 181-193.
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196.
E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7 (1969), pp. 231-242.
|
|
|
LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (6,-1)
Tanya Khovanova, Recursive Sequences
|
|
|
FORMULA
| a(n) = ((4+sqrt(2))/8)*(3+2*sqrt(2))^(n-1)+((4-sqrt(2))/8)*(3-2*sqrt(2))^(n-1). - Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar 29 2008
a(n) = A001653(n+1) - A001109(n). - Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar 29 2008
Sequence satisfies -7 = f(a(n), a(n+1)) where f(u, v) = u^2 + v^2 - 6*u*v. - Michael Somos Sep 28 2008
G.f.: (1 - 2*x) / (1 - 6*x + x^2). a(n) = (7 + a(n-1)^2) / a(n-2). - Michael Somos Sep 28 2008
|
|
|
MAPLE
| a[0]:=1: a[1]:=4: for n from 2 to 26 do a[n]:=6*a[n-1]-a[n-2] od: seq(a[n], n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 26 2006
|
|
|
PROG
| (PARI) {a(n) = real((3 + 2*quadgen(8))^n * (1 + quadgen(8) / 4))} /* Michael Somos Sep 28 2008 */
(PARI) {a(n) = polchebyshev(n, 1, 3) + polchebyshev(n-1, 2, 3)} /* Michael Somos Sep 28 2008 */
|
|
|
CROSSREFS
| Cf. A001653, A001541, A038725.
A038725(n) = a(-n).
Sequence in context: A144465 A024050 A193808 * A091640 A067110 A158197
Adjacent sequences: A038720 A038721 A038722 * A038724 A038725 A038726
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Barry E. Williams, May 02 2000
|
|
|
EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 03 2000
|
| |
|
|
