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A173779 A product triangle made from a cubic vector Markov sequence based on:q=4:M = {{0, 1, 0}, {0, 0, 1}, {q^3, q^3, 0}} 0
1, 1, 1, 1, 1, 1, 1, 128, 128, 1, 1, 128, 16384, 128, 1, 1, 8256, 1056768, 1056768, 8256, 1, 1, 16384, 135266304, 135266304, 135266304, 16384, 1, 1, 536576, 8791261184, 567036346368, 567036346368, 8791261184, 536576, 1, 1, 1576960, 846158888960 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are:

{1, 2, 3, 258, 16642, 2130050, 405831682, 1151656288258, 7204196783759362,

60358182097405870082, 985191616576574013308930,...}.

LINKS

Table of n, a(n) for n=0..38.

FORMULA

q=4:

M = {{0, 1, 0},

{0, 0, 1},

{q^3, q^3, 0}};

v(n)=v(n-1).M;

c(n)=Product(v(i)[[1]],{i,0,n}];

t(n,m)=c(n)/(c(m)*c(n-m))

EXAMPLE

{1},

{1, 1},

{1, 1, 1},

{1, 128, 128, 1},

{1, 128, 16384, 128, 1},

{1, 8256, 1056768, 1056768, 8256, 1},

{1, 16384, 135266304, 135266304, 135266304, 16384, 1},

{1, 536576, 8791261184, 567036346368, 567036346368, 8791261184, 536576, 1},

{1, 1576960, 846158888960, 108308337786880, 6985887787253760, 108308337786880, 846158888960, 1576960, 1},

{1, 35389440, 55807731302400, 233946009619660800, 29945089231316582400, 29945089231316582400, 233946009619660800, 55807731302400, 35389440, 1},

{1, 135266304, 4786998749429760, 58975824592974643200, 247226656693749704294400, 490620341965890886041600, 247226656693749704294400, 58975824592974643200, 4786998749429760, 135266304, 1}

MATHEMATICA

Clear[M, v, n, q, a, c, t];

M = {{0, 1, 0}, {0, 0, 1}, {q^3, q^3, 0}};

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

v[n_, q_] := v[n, q] = M.v[n - 1, q];

c[n_, q_] := Product[v[i, q][[1]], {i, 0, n}];

Table[Table[c[n, q], {n, 0, 10}], {q, 1, 10}];

t[n_, m_, q_] := c[n, q]/(c[m, q]*c[n - m, q]);

Table[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}], {q, 1, 10}];

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]

CROSSREFS

Sequence in context: A160638 A188829 A172532 * A187353 A248773 A217847

Adjacent sequences:  A173776 A173777 A173778 * A173780 A173781 A173782

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 24 2010

STATUS

approved

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Last modified August 21 15:56 EDT 2017. Contains 290890 sequences.