A173152 Triangle T(n,m) read by rows: T(n,0)=T(n,n)=1, else T(n,m)= binomial(n,m) + 2^(2*n-3) *binomial(n-2,m-1).

1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 36, 70, 36, 1, 1, 133, 394, 394, 133, 1, 1, 518, 2063, 3092, 2063, 518, 1, 1, 2055, 10261, 20515, 20515, 10261, 2055, 1, 1, 8200, 49180, 122936, 163910, 122936, 49180, 8200, 1, 1, 32777, 229412, 688212, 1147006, 1147006

Offset

0,5

Comments

Row sums are 1, 2, 6, 24, 144, 1056, 8256, 65664, 524544, 4194816, 3355545,...

Links

Table of n, a(n) for n=0..50.

Example

1;
1, 1;
1, 4, 1;
1, 11, 11, 1;
1, 36, 70, 36, 1;
1, 133, 394, 394, 133, 1;
1, 518, 2063, 3092, 2063, 518, 1;
1, 2055, 10261, 20515, 20515, 10261, 2055, 1;
1, 8200, 49180, 122936, 163910, 122936, 49180, 8200, 1;
1, 32777, 229412, 688212, 1147006, 1147006, 688212, 229412, 32777, 1;
1, 131082, 1048621, 3670136, 7340242, 9175292, 7340242, 3670136, 1048621, 131082, 1;

Mathematica

t[n_, m_, q_] := If[m == 0 || m == n, 1, Binomial[n, m] + q^(2*n - 3)*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

cf. A008292

Sequence in context: A174036 A157221 A146967 * A156049 A192015 A205946

Adjacent sequences: A173149 A173150 A173151 * A173153 A173154 A173155

Keyword

nonn,tabl

Author

Roger L. Bagula, Feb 11 2010

Status

approved