|
| |
|
|
A123004
|
|
G.f. x^2/(1-2*x-25*x^2).
|
|
0
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
REFERENCES
| Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
|
|
|
FORMULA
| a(n)= 2*a(n-1) +25*a(n-2).
a(n)=((1+sqrt(26)^n-(1-sqrt(26))^n)/(2*sqrt(26)) [From Rolf Pleisch (r_pleisch(AT)gmx.ch), Jul 06 2009]
|
|
|
MATHEMATICA
| (* coefficient expansion*) l = 2; m = 5; p[x_] := -1 - l*x/m + x^2 q[x_] := ExpandAll[x^2*p[1/x]] Table[ SeriesCoefficient[ Series[x/q[x], {x, 0, 30}], n]*m^(n - 1), {n, 0, 30}] (* Binet/ recursion *)
f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == l*a[n - 1]/m + a[n - 2], a[0] == 0, a[1] == 1}, a[n], n][[1]] // FullSimplify] ; a = Table[Rationalize[N[f[n]*m^(n - 1), 100], 0], {n, 0, 25}]
Join[{a=0, b=1}, Table[c=2*b+25*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 01 2011*)
|
|
|
CROSSREFS
| Cf. A002534.
Sequence in context: A031918 A101231 A141949 * A062618 A128842 A028883
Adjacent sequences: A123001 A123002 A123003 * A123005 A123006 A123007
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 23 2006
|
|
|
EXTENSIONS
| Definition replaced by generating function - the Assoc. Eds. of the OEIS, Mar 27 2010
|
| |
|
|
