|
| |
|
|
A133826
|
|
Triangle whose rows are sequences of increasing and decreasing tetrahedral numbers: 1; 1,4,1; 1,4,10,4,1; ... .
|
|
1
| |
|
|
1, 1, 4, 1, 1, 4, 10, 4, 1, 1, 4, 10, 20, 10, 4, 1, 1, 4, 10, 20, 35, 20, 10, 4, 1, 1, 4, 10, 20, 35, 56, 35, 20, 10, 4, 1, 1, 4, 10, 20, 35, 56, 84, 56, 35, 20, 10, 4, 1, 1, 4, 10, 20, 35, 56, 84, 120, 84, 56, 35, 20, 10, 4, 1, 1, 4, 10, 20, 35, 56, 84, 120, 165, 120, 84, 56, 35, 20
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Reading the triangle by rows produces the sequence 1,1,4,1,1,4,10,4,1,..., analogous to the Smarandache crescendo pyramidal sequence A004737.
|
|
|
FORMULA
| O.g.f.: (1+qx)/((1-x)(1-qx)^3(1-q^2x)) = 1 + x(1 + 4q + q^2) + x^2(1 + 4q + 10q^2 + 4q^3 + q^4) + ... .
|
|
|
EXAMPLE
| Triangle starts
1;
1, 4, 1;
1, 4, 10, 4, 1;
1, 4, 10, 20, 10, 4, 1;
|
|
|
CROSSREFS
| Cf. A000292, A002415 (row sums), A004737, A124258, A133825.
Sequence in context: A080061 A124258 A001638 * A122185 A193752 A136680
Adjacent sequences: A133823 A133824 A133825 * A133827 A133828 A133829
|
|
|
KEYWORD
| easy,nonn,tabl
|
|
|
AUTHOR
| Peter Bala (pbala(AT)toucansurf.com), Sep 25 2007
|
| |
|
|
