|
Search: id:A123004
|
|
|
| A123004 |
|
Scaled recursion, coefficient expansion and Binet for what I call a "Tin mean": Characteristic polynomial :l = 2; m = 5; x^2-l*x/m-1. |
|
+0
1
|
|
| 0, 1, 2, 29, 108, 941, 4582, 32689, 179928, 1177081, 6852362, 43131749, 257572548, 1593438821, 9626191342, 59088353209, 358831489968, 2194871810161, 13360530869522, 81592856993069, 497198985724188, 3034219396275101
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
To distinguish these from the "Lead" means as x^2-x/m-1 I call these "tin" as being rationally closer to whole Integers and thus being worth more? l=2; m=3; gives A002534
|
|
REFERENCES
|
Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
|
|
FORMULA
|
l = 2; m = 5; a(n) = l*a(n - 1)/m + a(n - 2) C.F.=x/(1 - 2 x/5 - x^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}]
|
|
CROSSREFS
|
Cf. A002534.
Sequence in context: A031918 A101231 A141949 this_sequence A062618 A128842 A028883
Adjacent sequences: A123001 A123002 A123003 this_sequence A123005 A123006 A123007
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 23 2006
|
|
|
Search completed in 0.002 seconds
|
