0,5

One of a family of Pascal-like arrays. A007318 is equivalent to the (1,0,1)-array. A008288 is equivalent to the (1,1,1)-array. Rows include A016777, A038764, A081583, A081584. Coefficients of the row polynomials in the Newton basis are given by A013610.

As a number triangle, this is the Riordan array (1/(1-x), x(1+2x)/(1-x)). It has row sums A002605 and diagonal sums A077947. - Paul Barry (pbarry(AT)wit.ie), Jan 24 2005

All entries are == 1 mod 3. - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 04 2008

Row sums are A002605. - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 09 2008)

Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.

Square array T(n, k) defined by T(n, 0) = T(0, k) = 1, T(n, k) = T(n, k-1)+2T(n-1, k-1)+T(n-1, k). Rows are the expansions of (1+2x)^k/(1-x)^(k+1).

G.f.: 1/(1-x-y-2xy). - Ralf Stephan, Apr 28 2004

T(n,k)=sum{j=0..n, C(k,j-k)*C(n+k-j,k)*2^(j-k)}; - Paul Barry (pbarry(AT)wit.ie), Oct 23 2006

a(n)=2*{0,a(n-2),0}+{0,a(n-1)}+{a(n-1),0}. [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 09 2008]

Rows begin

1 1 1 1 1 ...

1 4 7 10 13 ...

1 7 22 46 79 ...

1 10 46 136 307 ...

1 13 79 307 886 ...

Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 09 2008: (Start) As a triangle this begins:

{1},

{1, 1},

{1, 4, 1},

{1, 7, 7, 1},

{1, 10, 22, 10, 1},

{1, 13, 46, 46, 13, 1},

{1, 16, 79, 136, 79, 16, 1},

{1, 19, 121, 307, 307, 121, 19, 1},

{1, 22, 172, 586, 886, 586, 172, 22, 1},

{1, 25, 232, 1000, 2086, 2086, 1000, 232, 25, 1},

{1, 28, 301, 1576, 4258, 5944, 4258, 1576, 301, 28, 1} (End)

{1, 28, 301, 1576, 4258, 5944, 4258, 1576, 301, 28, 1} (End)

...

Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 09 2008: (Start)

Clear[a]; a[0] = {1}; a[1] = {1, 1};

a[n_] := a[n] = 2*Join[{0}, a[n - 2], {0}] + Join[{0}, a[n - 1]] + Join[a[n - 1], {0}];

Table[a[n], {n, 0, 10}]; Flatten[%] (End)

Cf. A081578, A081579, A081580.

A008288 [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 09 2008]

Sequence in context: A131060 A124376 A047671 this_sequence A146986 A146771 A073697

Adjacent sequences: A081574 A081575 A081576 this_sequence A081578 A081579 A081580

easy,nonn,tabl

Paul Barry (pbarry(AT)wit.ie), Mar 23 2003