|
Search: id:A122767
|
|
|
| A122767 |
|
Scaled coefficient expansion of second derivative of Steinbach polynomial: -1+ 3 x + 3 x^2 - 4 x^3 - x^4 + x^5 Second derivative: 6 - 24 x - 12 x^2 + 20 x^3 C.F.=x/(20 - 12 x - 24 x^2 + 6 x^3). |
|
+0
2
|
|
| 0, 2, 12, 312, 2712, 50112, 532512, 8394912, 99237312, 1443059712, 18048362112, 251686144512, 3243002406912, 44245843149312, 579129504371712, 7811377482074112, 103090052472256512, 1382166761370918912
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Roots are real: a0 = Table[x /. NSolve[p[x] == 0, x][[n]], {n, 1, 3}] {-0.96523, 0.233361, 1.33187}
|
|
REFERENCES
|
P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
|
|
FORMULA
|
C.F.=x/(20 - 12 x - 24 x^2 + 6 x^3)
|
|
MATHEMATICA
|
p[x_] := 6 - 24 x - 12 x^2 + 20 x^3 q[x_] := ExpandAll[x^3*p[1/x]] Table[ 20*SeriesCoefficient[ Series[x/q[x], {x, 0, 30}], n]*2^n*5^(n - 1), {n, 0, 30}]
|
|
CROSSREFS
|
Cf. A122601, A078008.
Sequence in context: A012377 A012425 A012422 this_sequence A094047 A091472 A156518
Adjacent sequences: A122764 A122765 A122766 this_sequence A122768 A122769 A122770
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 22 2006
|
|
|
Search completed in 0.002 seconds
|
