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A173077 Triangle read by rows: q=3;t(n,m,q)=If[m == 0 || m == n, 1, Binomial[n, m] - 1 + (q^ Floor[n/2])*Binomial[n - 2, m - 1]] 0
1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 12, 23, 12, 1, 1, 13, 36, 36, 13, 1, 1, 32, 122, 181, 122, 32, 1, 1, 33, 155, 304, 304, 155, 33, 1, 1, 88, 513, 1270, 1689, 1270, 513, 88, 1, 1, 89, 602, 1784, 2960, 2960, 1784, 602, 89, 1, 1, 252, 1988, 6923, 13817, 17261, 13817, 6923 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 6, 12, 49, 100, 491, 986, 5433, 10872, 63223,...}.

LINKS

Table of n, a(n) for n=0..62.

FORMULA

q=3;

t(n,m,q)=If[m == 0 || m == n, 1, Binomial[n, m] - 1 + (q^ Floor[n/2])*Binomial[n - 2, m - 1]]

EXAMPLE

{1},

{1, 1},

{1, 4, 1},

{1, 5, 5, 1},

{1, 12, 23, 12, 1},

{1, 13, 36, 36, 13, 1},

{1, 32, 122, 181, 122, 32, 1},

{1, 33, 155, 304, 304, 155, 33, 1},

{1, 88, 513, 1270, 1689, 1270, 513, 88, 1},

{1, 89, 602, 1784, 2960, 2960, 1784, 602, 89, 1},

{1, 252, 1988, 6923, 13817, 17261, 13817, 6923, 1988, 252, 1}

MATHEMATICA

Clear[t, n, m, q];

t[n_, m_, q_] := If[m == 0 || m == n, 1, Binomial[n, m] - 1 + (q^Floor[n/2])*Binomial[n - 2, m - 1]];

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: A166455 A171142 A174037 * A131239 A114033 A209417

Adjacent sequences:  A173074 A173075 A173076 * A173078 A173079 A173080

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 09 2010

STATUS

approved

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Last modified July 15 16:29 EDT 2019. Contains 325049 sequences. (Running on oeis4.)