_Roger L. Bagula_, Dec 08 2010

_Roger Bagula (rlbagulatftn(AT)yahoo.com), _, Dec 08 2010

reviewed

approved

proposed

reviewed

A triangle sequence:Triangle t(n,m) =Binomial binomial(n + (m - 1), (,m - 1)) - Binomialbinomial(n - (m - 1), (,m - ), 1))<=m<=n, read by rows.

Row sums are: { binomial(2n+1,n+1)-1-A000071(n+1) = A001700(n)-A000045(n+1) = 2, 8, 32, 121, 454, 1703, 6414, 24276, 92323, 352627,...}.

t(n,m) =Binomial A046899(n + (m - 1), (,m - 1)) - BinomialA011973(n - (,m - 1), (0<=m - 1))<=n/2.

{2},

2;

{2, 6},;

{2, 10, 20},;

{2, 14, 35, 70},;

{2, 18, 56, 126, 252},;

{2, 22, 83, 210, 462, 924},;

{2, 26, 116, 330, 792, 1716, 3432},;

{2, 30, 155, 494, 1287, 3003, 6435, 12870},;

{2, 34, 200, 710, 2002, 5005, 11440, 24310, 48620},;

{2, 38, 251, 986, 3002, 8008, 19448, 43758, 92378, 184756};

Cf. A046899, A178300, A001791

allocated for Roger Bagula

A triangle sequence:t(n,m)=Binomial(n + (m - 1), (m - 1)) - Binomial(n - (m - 1), (m - 1))

2, 2, 6, 2, 10, 20, 2, 14, 35, 70, 2, 18, 56, 126, 252, 2, 22, 83, 210, 462, 924, 2, 26, 116, 330, 792, 1716, 3432, 2, 30, 155, 494, 1287, 3003, 6435, 12870, 2, 34, 200, 710, 2002, 5005, 11440, 24310, 48620, 2, 38, 251, 986, 3002, 8008, 19448, 43758, 92378, 184756

1,1

Row sums are: {2, 8, 32, 121, 454, 1703, 6414, 24276, 92323, 352627,...}.

t(n,m)=Binomial(n + (m - 1), (m - 1)) - Binomial(n - (m - 1), (m - 1))

{2},

{2, 6},

{2, 10, 20},

{2, 14, 35, 70},

{2, 18, 56, 126, 252},

{2, 22, 83, 210, 462, 924},

{2, 26, 116, 330, 792, 1716, 3432},

{2, 30, 155, 494, 1287, 3003, 6435, 12870},

{2, 34, 200, 710, 2002, 5005, 11440, 24310, 48620},

{2, 38, 251, 986, 3002, 8008, 19448, 43758, 92378, 184756}

t[n_, m_] = Binomial[n + (m - 1), (m - 1)] - Binomial[n - (m - 1), (m - 1)];

Table[Table[t[n, m], {m, 2, n + 1}], {n, 1, 10}];

Flatten[%]

Cf. A046899,A178300,A001791

allocated

nonn,tabl

Roger Bagula (rlbagulatftn(AT)yahoo.com), Dec 08 2010

approved

proposed

allocated for Roger Bagula

recycled

allocated

recycled

approved