|
Search: id:A139524
|
|
|
| A139524 |
|
A trinomial made into a single varaiabe polynomial coefficient triangle form three Pascal binomials in {x,y},{y,z} and {x,z}: binomials as: f(x,y,n)=Sum[Binomial[n, i]*x^i*y^(n - i), {i, 0, n}]; p(x,y,z,n)=f(x,y,n)+f(y,z,n)+f(x,z,n). |
|
+0
1
|
|
| 3, 4, 2, 6, 4, 2, 10, 6, 6, 2, 18, 8, 12, 8, 2, 34, 10, 20, 20, 10, 2, 66, 12, 30, 40, 30, 12, 2, 130, 14, 42, 70, 70, 42, 14, 2, 258, 16, 56, 112, 140, 112, 56, 16, 2, 514, 18, 72, 168, 252, 252, 168, 72, 18, 2, 1026, 20, 90, 240, 420, 504, 420, 240, 90, 20, 2
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Row sums are A007283.
|
|
REFERENCES
|
Advanced Number Theory, Harvey Cohn, Dover Books, 1963, Pages 88-89
|
|
FORMULA
|
f(x,y,n)=Sum[Binomial[n, i]*x^i*y^(n - i), {i, 0, n}]; p(x,y,z,n)=f(x,y,n)+f(y,z,n)+f(x,z,n); Out_n,m=Coefficients(p(x,1,1,n)).
|
|
EXAMPLE
|
{3},
{4, 2},
{6, 4, 2},
{10, 6, 6, 2},
{18, 8, 12, 8, 2},
{34, 10, 20, 20, 10, 2},
{66, 12, 30, 40, 30, 12, 2},
{130, 14, 42, 70, 70, 42, 14, 2},
{258, 16, 56, 112, 140, 112, 56, 16, 2},
{514, 18, 72, 168, 252, 252, 168, 72, 18, 2},
{1026, 20, 90, 240, 420, 504, 420, 240, 90, 20, 2}
|
|
MATHEMATICA
|
Clear[f, x, n] f[x_, y_, n_] = Sum[Binomial[n, i]*x^i*y^(n - i), {i, 0, n}]; Table[ExpandAll[f[x, y, n] + f[y, z, n] + f[x, z, n]], {n, 0, 10}] a = Table[CoefficientList[ExpandAll[f[x, y, n] + f[y, z, n] + f[x, z, n]] /. y -> 1 /. z -> 1, x], {n, 0, 10}]; Flatten[a]
|
|
CROSSREFS
|
Cf. A007283.
Sequence in context: A154570 A145961 A082928 this_sequence A108127 A049277 A143052
Adjacent sequences: A139521 A139522 A139523 this_sequence A139525 A139526 A139527
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jun 09 2008
|
|
|
Search completed in 0.002 seconds
|
