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

1,2

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, ...

Links

Table of n, a(n) for n=1..78.

Formula

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

Example

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.

Sequence in context: A099508 A141577 A245142 * A237113 A293937 A291857

Adjacent sequences: A123312 A123313 A123314 * A123316 A123317 A123318

Keyword

easy,nonn,tabl,word

Author

Jonathan Vos Post, Nov 08 2006

Status

approved