|
Search: id:A137370
|
|
|
| A137370 |
|
Brahmagupta matrix in a Markov matrix recursion produces a set of poylnomials: the special values of x->Sqrt[z];y->1;t->n gives a set of polynomials as determinants. The triangular sequence of the Coefficients of these polynomials are except for signs A055134. |
|
+0
1
|
|
| 1, 0, 1, 1, -2, 1, -8, 12, -6, 1, 81, -108, 54, -12, 1, -1024, 1280, -640, 160, -20, 1, 15625, -18750, 9375, -2500, 375, -30, 1, -279936, 326592, -163296, 45360, -7560, 756, -42, 1, 5764801, -6588344, 3294172, -941192, 168070, -19208, 1372, -56, 1, -134217728, 150994944, -75497472, 22020096, -4128768
(list; table; graph; listen)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
Row sums are: {1, 1, 0, -1, 16, -243, 4096, -78125, 1679616, -40353607, 1073741824, -31381059609}
|
|
REFERENCES
|
Weisstein, Eric W. "Brahmagupta Matrix." http://mathworld.wolfram.com/BrahmaguptaMatrix.html
|
|
FORMULA
|
b(0)={{x,y},{t*y,x}}; b(n)=b(n-1).b(0) p(z,n)=Det[b(n));x->Sqrt[z];y->1;t->n
|
|
EXAMPLE
|
{1},
{0, 1},
{1, -2, 1},
{-8, 12, -6, 1},
{81, -108, 54, -12, 1},
{-1024, 1280, -640, 160, -20, 1},
{15625, -18750, 9375, -2500, 375, -30, 1},
{-279936, 326592, -163296, 45360, -7560, 756, -42, 1},
{5764801, -6588344, 3294172, -941192, 168070, -19208, 1372, -56, 1}, {-134217728, 150994944, -75497472, 22020096, -4128768, 516096, -43008, 2304, -72, 1},
{3486784401, -3874204890,1937102445, -573956280, 111602610, -14880348, 1377810, -87480, 3645, -90,1},
{-100000000000, 110000000000, -55000000000, 16500000000, -3300000000, \462000000, -46200000, 3300000, -165000, 5500, -110, 1}
|
|
MATHEMATICA
|
Clear[B] B[0] = {{x, y}, {t*y, x}}; B[n_] := B[n] = B[n - 1].B[0]; Table[Det[B[n]] /. x -> Sqrt[z] /. y -> 1 /. t -> n, {n, 0, 10}]; a = Join[{{1}}, Table[CoefficientList[Det[B[n]] /. x -> Sqrt[z] /. y ->1 /. t -> n, z], {n, 0, 10}]]; Flatten[a]
|
|
CROSSREFS
|
Adjacent sequences: A137367 A137368 A137369 this_sequence A137371 A137372 A137373
Sequence in context: A007026 A118708 A055134 this_sequence A151501 A102735 A088960
|
|
KEYWORD
|
uned,tabl,sign
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 09 2008
|
|
|
Search completed in 0.002 seconds
|
