1,5

Row sums are:

{1, 2, 4, 10, 26, 62, 133, 260, 471, 802, 1298}.

Contribution from Paul Barry (pbarry(AT)wit.ie), Jan 07 2009: (Start)

This triangle follows a general construction method as follows: Let a(n) be an integer sequence

with a(0)=1, a(1)=1. Then T(n,k,r):=[k<=n](1+r*a(k)*a(n-k)) defines a symmetrical triangle.

Row sums are n+1+r*sum{k=0..n, a(k)*a(n-k)} and central coefficients are 1+r*a(n)^2.

Here a(n)=C(n+1,2) and r=1.

Row sums are A154322 and central coefficients are A154323. (End)

t(n,m)=(n - m)*(n - m + 1)*m*(m + 1)/4 + 1.

{1},

{1, 1},

{1, 2, 1},

{1, 4, 4, 1},

{1, 7, 10, 7, 1},

{1, 11, 19, 19, 11, 1},

{1, 16, 31, 37, 31, 16, 1},

{1, 22, 46, 61, 61, 46, 22, 1},

{1, 29, 64, 91, 101, 91, 64, 29, 1},

{1, 37, 85, 127, 151, 151, 127, 85, 37, 1},

{1, 46, 109, 169, 211, 226, 211, 169, 109, 46, 1}

Clear[t, n, m] t[n_, m_] = (n - m)*(n - m + 1)*m*(m + 1)/4 + 1; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Sequence in context: A161126 A128562 A034368 this_sequence A118245 A104382 A086629

Adjacent sequences: A113579 A113580 A113581 this_sequence A113583 A113584 A113585

nonn,tabl

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Aug 25 2008