|
|
A123004
|
|
Expansion of g.f. x^2/(1 - 2*x - 25*x^2).
|
|
4
|
|
|
0, 1, 2, 29, 108, 941, 4582, 32689, 179928, 1177081, 6852362, 43131749, 257572548, 1593438821, 9626191342, 59088353209, 358831489968, 2194871810161, 13360530869522, 81592856993069, 497198985724188, 3034219396275101
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
REFERENCES
|
Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2*a(n-1) + 25*a(n-2).
a(n) = ((1+sqrt(26)^n - (1-sqrt(26))^n)/(2*sqrt(26)). - Rolf Pleisch, Jul 06 2009
a(n) = (5*i)^(n-2)*ChebyshevU(n-2, -i/5). - G. C. Greubel, Jul 12 2021
|
|
MATHEMATICA
|
Rest@CoefficientList[Series[x^2/(1 -2*x -25*x^2), {x, 0, 40}], x]
|
|
PROG
|
(Magma) [n le 2 select n-1 else 2*Self(n-1) +25*Self(n-2): n in [1..30]]; // G. C. Greubel, Jul 12 2021
(Sage) [(5*i)^(n-2)*chebyshev_U(n-2, -i/5) for n in [1..30]] # G. C. Greubel, Jul 12 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Definition replaced by generating function - the Assoc. Eds. of the OEIS, Mar 27 2010
|
|
STATUS
|
approved
|
|
|
|