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A167925 A triangular sequence of the Matrix Markov type based on the 2x2 matrix: m={{a,1},{-1,1}}; which has determinant equal to trace. 1
0, 1, 1, 1, 2, 3, 0, 2, 6, 12, -1, 0, 9, 32, 75, -1, -4, 9, 80, 275, 684, 0, -8, 0, 192, 1000, 3240, 8232, 1, -8, -27, 448, 3625, 15336, 47677, 122368, 1, 0, -81, 1024, 13125, 72576, 276115, 835584, 2158569, 0, 16, -162, 2304, 47500, 343440, 1599066 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{0, 2, 6, 20, 115, 1043, 12656, 189420, 3356913, 68661516, 1591360540,...}

Each row is a specific Markov sequence with a different limiting ratio.

Conjecture: a(6),a(7),a(8),a(9)=coefficient of x^2 in the Maclaurin expansion of 1/(n*x^2+n*x+1) for n=1,2,3,4; a(10),a(11),a(12),a(13),a(14)=-coefficient of x^3 in the Maclaurin expansion of 1/(n*x^2+n*x+1) for n=1,2,3,4,5; a(15),a(16),a(17),a(18),a(19),a(20)=coefficient of x^4 in the Maclaurin expansion of 1/(n*x^2+n*x+1) for n=1,2,3,4,5,6; a(21),a(22),a(23),a(24),a(25),a(26),a(27)=-coefficient of x^5 in the Maclaurin expansion of 1/(n*x^2+n*x+1) for n=1,2,3,4,5,6,7. Etc... [From Francesco Daddi, Aug 04 2011]

LINKS

Table of n, a(n) for n=0..51.

EXAMPLE

{0},

{1, 1},

{1, 2, 3},

{0, 2, 6, 12},

{-1, 0, 9, 32, 75},

{-1, -4, 9, 80, 275, 684},

{0, -8, 0, 192, 1000, 3240, 8232},

{1, -8, -27, 448, 3625, 15336, 47677, 122368},

{1, 0, -81, 1024, 13125, 72576, 276115, 835584, 2158569},

{0, 16, -162, 2304, 47500, 343440, 1599066, 5705728, 16953624, 44010000},

{-1, 32, -243, 5120, 171875, 1625184, 9260657, 38961152, 133155495, 390500000, 1017681269}

MATHEMATICA

Clear[m, a, n, v];

m = {{a, 1}, {-1, 1}};

v[0] := {0, 1};

v[n_] := v[n] = m.v[n - 1];

Table[v[n][[1]], {n, 0, 10}, {a, 0, n}];

Flatten[%]

CROSSREFS

Sequence in context: A248342 A002392 A002708 * A209927 A059283 A160202

Adjacent sequences:  A167922 A167923 A167924 * A167926 A167927 A167928

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Nov 15 2009

STATUS

approved

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Last modified December 19 01:55 EST 2014. Contains 252175 sequences.