A258197 Arithmetic derivative of Pascal's triangle.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 4, 5, 4, 0, 0, 1, 7, 7, 1, 0, 0, 5, 8, 24, 8, 5, 0, 0, 1, 10, 12, 12, 10, 1, 0, 0, 12, 32, 92, 59, 92, 32, 12, 0, 0, 6, 60, 124, 165, 165, 124, 60, 6, 0, 0, 7, 39, 244, 247, 456, 247, 244, 39, 7, 0, 0, 1, 16, 103, 371, 493

Offset

0,12

Comments

T(n,k) = A003415(A007318(n,k)), 0 <= k <= n;

for n > 0: T(n,1) = A003415(n));

for n > 1: T(n,2) = A068312(n)).

A258318(n) = number of distinct terms up to row n.

Links

Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Example

.  First 10 rows:                     |           Pascal's triangle
.  0:  0                              |  1
.  1:  0,0                            |  1,1
.  2:  0,1,0                          |  1,2,1
.  3:  0,1,1,0                        |  1,3,3,1
.  4:  0,4,5,4,0                      |  1,4,6,4,1
.  5:  0,1,7,7,1,0                    |  1,5,10,10,5,1
.  6:  0,5,8,24,8,5,0                 |  1,6,15,20,15,6,1
.  7:  0,1,10,12,12,10,1,0            |  1,7,21,35,35,21,7,1
.  8:  0,12,32,92,59,92,32,12,0       |  1,8,28,56,70,56,28,8,1
.  9:  0,6,60,124,165,165,124,60,6,0  |  1,9,36,84,126,126,84,36,9,1 .

Prog

(Haskell)
a258197 n k = a258197_tabl !! n !! k
a258197_row n = a258197_tabl !! n
a258197_tabl = map (map a003415) a007318_tabl

Crossrefs

Cf. A003415, A007318, A258290 (central terms), A258317 (row sums), A068312, A258318.

Sequence in context: A020503 A307484 A266964 * A255698 A290558 A071992

Adjacent sequences: A258194 A258195 A258196 * A258198 A258199 A258200

Keyword

nonn,tabl

Author

Reinhard Zumkeller, May 26 2015

Status

approved