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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 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.)