A177877 Triangle in which row n is derived from (1,2,3,...,n) dot (n,n-1,...,1) with additive carryovers.

1, 2, 4, 3, 7, 10, 4, 10, 16, 20, 5, 13, 22, 30, 35, 6, 16, 28, 40, 50, 56, 7, 19, 34, 50, 65, 77, 84, 8, 22, 40, 60, 80, 98, 112, 120, 9, 25, 46, 70, 95, 119, 140, 156, 165, 10, 28, 52, 80, 110, 140, 168, 192, 210, 220

Offset

0,2

Comments

Carryovers (additive) are defined as "add current product to next product". For example: (1,2,3) dot (3,2,1) with carryovers = ((1*3=3 ), (2*2+3=7), (1*3+7=10), so row 2 = (3, 7, 10).

Row sums = A002415: (1, 6, 20, 50, 105, 196,...)

Links

Table of n, a(n) for n=0..54.

Formula

By rows, (1,2,3,...) dot (...3,2,1); add current product to next product.

As an array, row 0 = the tetrahedral numbers, (1, 4, 10, 20, 35,...). n-th row adds n*(1, 3, 6, 10, 15,...) termwise.

Example

Row 2 = (3, 7, 10) = (1, 2, 3) dot (3, 2, 1) with carryovers, thus: (3 = 1*3; 7 = 2*2 + 3; 10 = 3*1 + 7.
First few rows of the array =
1,...4,..10,..20,..35,...
2,...7,..16,..30,..50,...
3,..10,..22,..40,..65,...
...
Example: row 1 is obtained by adding (1, 3, 6, 10, 15,...) termwise to (1, 4, 10, 20, 35,...).
First few rows of the triangle =
.
1;
2, 4;
3, 7, 10;
4, 10, 16, 20;
5, 13, 22, 30, 35;
6, 16, 28, 40, 50, 56;
7, 19, 34, 50, 65, 77, 84;
8, 22, 40, 60, 80, 98, 112, 120;
9, 25, 46, 70, 95, 119, 140, 156, 165;
10, 28, 52 80, 110, 140, 168, 192, 210, 220;
...

Crossrefs

Cf. A002415

Sequence in context: A246267 A101267 A207633 * A090568 A329877 A223625

Adjacent sequences: A177874 A177875 A177876 * A177878 A177879 A177880

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 13 2010

Status

approved