A123315 Pascrabble triangle, read by rows.

1, 3, 3, 8, 10, 8, 9, 12, 12, 9, 4, 15, 19, 15, 4, 7, 15, 19, 19, 15, 7, 8, 18, 19, 21, 19, 18, 8, 9, 22, 20, 11, 11, 20, 22, 9, 4, 15, 17, 15, 18, 15, 17, 15, 4, 7, 15, 18, 18, 20, 20, 18, 18, 15, 7, 8, 18, 20, 22, 21, 11, 21, 22, 20, 18, 8, 9, 22, 21, 17, 19, 18, 18, 19, 17, 21, 22, 9

Offset: 1

Author

Jonathan Vos Post, Nov 08 2006

Keywords

• easy
• nonn
• tabl
• word

Comments

The apex of the triangle is 1. Any other value is the Scrabble value of English name for the number which is the sum of the numbers above. This is generated the same way as A007318 Pascal's triangle read by rows, except apply A113172 to each sum. The first column of this triangle is 1, 3, 8, 9, 4, 7, 8, 9, 4, 7, 8, 9, 4, 7... = iterations 1, A113172(1), A113172(A113172(1)), A113172(A113172(A113172(1))). The central pascrabble numbers T(2n+1,n) = 1, 10, 19, 21, 18, 11, 22, ...

Examples

			Triangle begins:
row.|.values in row
.1..|01
.2..|03.03
.3..|08.10.08
.4..|09.12.12.09
.5..|04.15.19.15.04
.6..|07.15.19.19.15.07
.7..|08.18.19.21.19.18.08
.8..|09.22.20.11.11.20.22.09
.9..|04.15.17.15.18.15.17.15.04
10..|07.15.18.18.20.20.18.18.15.07
11..|08.18.20.22.21.11.21.22.20.18.8
12..|09.22.21.17.19.18.18.19.17.21.22.09
		

Crossrefs

Cf. A007318 Pascal's triangle read by rows, A113172.

Formula

T(1,1) = 1; for i > 1, T(i,j) = A113172(T(i-1, j-1)+T(i-1, j)).