A245099 Triangle read by rows: T(n,k) = A024916(k)*A002865(n-k).

1, 0, 4, 1, 0, 8, 1, 4, 0, 15, 2, 4, 8, 0, 21, 2, 8, 8, 15, 0, 33, 4, 8, 16, 15, 21, 0, 41, 4, 16, 16, 30, 21, 33, 0, 56, 7, 16, 32, 30, 42, 33, 41, 0, 69, 8, 28, 32, 60, 42, 66, 41, 56, 0, 87, 12, 32, 56, 60, 84, 66, 82, 56, 69, 0, 99, 14, 48, 64

Offset

1,3

Comments

Row sums give A066186.

Column 1 is A002865.

Leading diagonal is A024916.

Since A024916(k) has a symmetric representation then both T(n,k) and the partial sums of row n can be represented by symmetric polycubes - for more information see A237593 and A237270. For another version see A221529.

Links

Table of n, a(n) for n=1..69.

Example

Triangle begins:
1;
0,   4;
1,   0,  8;
1,   4,  0, 15;
2,   4,  8,  0, 21;
2,   8,  8, 15,  0, 33;
4,   8, 16, 15, 21,  0, 41;
4,  16, 16, 30, 21, 33,  0, 56;
7,  16, 32, 30, 42, 33, 41,  0, 69;
8,  28, 32, 60, 42, 66, 41, 56,  0, 87;
12, 32, 56, 60, 84, 66, 82, 56, 69,  0, 99;
...
For n = 6:
-------------------------
k   A024916        T(6,k)
-------------------------
1      1  *  2   =    2
2      4  *  2   =    8
3      8  *  1   =    8
4     15  *  1   =   15
5     21  *  0   =    0
6     33  *  1   =   33
.         A002865
-------------------------
So row 6 is [2, 8, 8, 15, 0, 33] and the sum of row 6 is 2+8+8+15+0+33 = 66 equaling A066186(6) = 6*A000041(6) = 6*11 = 66.

Crossrefs

Cf. A000041, A000203, A002865, A024916, A066186, A221529, A221530, A245095.

Sequence in context: A198215 A062175 A085659 * A176219 A231350 A152420

Adjacent sequences: A245096 A245097 A245098 * A245100 A245101 A245102

Keyword

nonn,tabl

Author

Omar E. Pol, Jul 13 2014

Status

approved