A157343 Triangle T(n,k) read by rows: T(n,k)=1 if the row index n is prime or <=1, otherwise T(n,k) = T(n-1,k)+T(n-1,k-1).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 3, 4, 4, 4, 4, 4, 4, 3, 1, 1, 4, 7, 8, 8, 8, 8, 8, 7, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,12

Comments

Row sums are: 1, 2, 3, 4, 8, 6, 12, 8, 16, 32, 64, 12, 24, 14, 28, 56,...

Links

Table of n, a(n) for n=0..104.

Example

1;
1, 1;
1, 1, 1;
1, 1, 1, 1;
1, 2, 2, 2, 1;
1, 1, 1, 1, 1, 1;
1, 2, 2, 2, 2, 2, 1;
1, 1, 1, 1, 1, 1, 1, 1;
1, 2, 2, 2, 2, 2, 2, 2, 1;
1, 3, 4, 4, 4, 4, 4, 4, 3, 1;
1, 4, 7, 8, 8, 8, 8, 8, 7, 4, 1;
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1;
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1;
1, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 1;

Mathematica

Clear[p, x, n, a];
p[x, 0] = 1; p[x, 1] = ((x + 1)); p[x, 2] = ((x^2 + x + 1));
p[x_, n_] := p[x, n] = If[PrimeQ[n], Sum[x^i, {i, 0, n}], (x + 1)*p[x, n - 1]];
a = Table[CoefficientList[FullSimplify[p[x, n]], x], {n, 0, 15}];
Flatten[a]

Crossrefs

Sequence in context: A030597 A030599 A237413 * A102679 A025146 A067397

Adjacent sequences: A157340 A157341 A157342 * A157344 A157345 A157346

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Feb 27 2009

Status

approved