|
| |
|
|
A051958
|
|
a(n) = 2 a(n-1) + 24 a(n-2), a(0)=0, a(1)=1.
|
|
9
|
|
|
|
0, 1, 2, 28, 104, 880, 4256, 29632, 161408, 1033984, 5941760, 36699136, 216000512, 1312780288, 7809572864, 47125872640, 281681494016, 1694383931392, 10149123719168, 60963461791744, 365505892843520, 2194134868688896
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
The ratio a(n+1)/a(n) converges to 6 as n approaches infinity. - Felix P. Muga II, Mar 10 2014
|
|
|
REFERENCES
|
F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate.
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (2,24).
|
|
|
FORMULA
|
G.f.: x/((1+4*x)*(1-6*x)).
a(n) = (6^n - (-4)^n)/10.
a(n) = 2^(n-1)*A015441(n).
a(n+1) = Sum_{k = 0..n} A238801(n,k)*5^k. - Philippe Deléham, Mar 07 2014
|
|
|
MATHEMATICA
|
Join[{a=0, b=1}, Table[c=2*b+24*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[x / ((1 + 4 x) (1 - 6 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Mar 08 2014 *)
LinearRecurrence[{2, 24}, {0, 1}, 30] (* Harvey P. Dale, May 08 2022 *)
|
|
|
PROG
|
(PARI) a(n)=(6^n-(-4)^n)/10
(MAGMA) [(6^n-(-4)^n)/10: n in [0..25]]; // Vincenzo Librandi, Mar 08 2014
|
|
|
CROSSREFS
|
Cf. A015441.
Sequence in context: A200040 A334696 A281201 * A123807 A213829 A164834
Adjacent sequences: A051955 A051956 A051957 * A051959 A051960 A051961
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Barry E. Williams, Jan 04 2000
|
|
|
STATUS
|
approved
|
| |
|
|
