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A173741 A triangle of the form:q=2:t(n,m,q)=Binomial[n, m] + 2*q*If[m*(n - m) > 0, 1, If[(n - 2) *(m - 1) >= 1, Binomial[n - 2, m - 1], 0]] 0
1, 1, 1, 1, 6, 1, 1, 7, 7, 1, 1, 8, 10, 8, 1, 1, 9, 14, 14, 9, 1, 1, 10, 19, 24, 19, 10, 1, 1, 11, 25, 39, 39, 25, 11, 1, 1, 12, 32, 60, 74, 60, 32, 12, 1, 1, 13, 40, 88, 130, 130, 88, 40, 13, 1, 1, 14, 49, 124, 214, 256, 214, 124, 49, 14, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 8, 16, 28, 48, 84, 152, 284, 544, 1060,...}.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

q=2;

t(n,m,q)=Binomial[n, m] + 2*q*If[m*(n - m) > 0, 1, If[(n - 2) *(m - 1) >= 1, Binomial[n - 2, m - 1], 0]]

EXAMPLE

{1},

{1, 1},

{1, 6, 1},

{1, 7, 7, 1},

{1, 8, 10, 8, 1},

{1, 9, 14, 14, 9, 1},

{1, 10, 19, 24, 19, 10, 1},

{1, 11, 25, 39, 39, 25, 11, 1},

{1, 12, 32, 60, 74, 60, 32, 12, 1},

{1, 13, 40, 88, 130, 130, 88, 40, 13, 1},

{1, 14, 49, 124, 214, 256, 214, 124, 49, 14, 1}

MATHEMATICA

t[n_, m_, q_] = Binomial[n, m] + 2*q*If[m*(n - m) > 0, 1, If[(n - 2) *(m - 1) >= 1, Binomial[n - 2, m - 1], 0]];

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

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

CROSSREFS

Cf. A156050

Sequence in context: A176348 A176264 A195397 * A171147 A171695 A179233

Adjacent sequences:  A173738 A173739 A173740 * A173742 A173743 A173744

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 23 2010

STATUS

approved

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Last modified October 22 02:06 EDT 2017. Contains 293756 sequences.