|
| |
|
|
A055269
|
|
a(n)=4a(n-1)-a(n-2)+3; a(0)=1, a(1)=7.
|
|
0
| |
|
|
1, 7, 30, 116, 437, 1635, 6106, 22792, 85065, 317471, 1184822, 4421820, 16502461, 61588027, 229849650, 857810576, 3201392657, 11947760055, 44589647566, 166410830212, 621053673285
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7 (1969), pps. 181-193.
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 122-125, 194-196.
E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart.,7 (1969), pps. 231-242.
|
|
|
FORMULA
| a(n)={[(17-5*{2-sqrt(3)})(2+sqrt(3))^n+(5*{2+sqrt(3)}-17)(2-sqrt(3))^n]/[4*sqrt(3)]} -3/2.
|
|
|
EXAMPLE
| G.f.=(1+2x)/(1-x)(1-4x+x^2). Also the first partial sum of A054491.
|
|
|
CROSSREFS
| Cf. A001834 and A054491.
Sequence in context: A038798 A062455 A085277 * A026631 A037709 A037611
Adjacent sequences: A055266 A055267 A055268 * A055270 A055271 A055272
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Barry E. Williams, May 10 2000
|
|
|
EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
|
| |
|
|
