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A123315 Pascrabble triangle, read by rows.

%I A123315 #8 Sep 16 2024 09:19:59
%S A123315 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,
%T A123315 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,
%U A123315 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
%N A123315 Pascrabble triangle, read by rows.
%C A123315 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, ...
%F A123315 T(1,1) = 1; for i > 1, T(i,j) = A113172(T(i-1, j-1)+T(i-1, j)).
%e A123315 Triangle begins:
%e A123315 row.|.values in row
%e A123315 .1..|01
%e A123315 .2..|03.03
%e A123315 .3..|08.10.08
%e A123315 .4..|09.12.12.09
%e A123315 .5..|04.15.19.15.04
%e A123315 .6..|07.15.19.19.15.07
%e A123315 .7..|08.18.19.21.19.18.08
%e A123315 .8..|09.22.20.11.11.20.22.09
%e A123315 .9..|04.15.17.15.18.15.17.15.04
%e A123315 10..|07.15.18.18.20.20.18.18.15.07
%e A123315 11..|08.18.20.22.21.11.21.22.20.18.8
%e A123315 12..|09.22.21.17.19.18.18.19.17.21.22.09
%Y A123315 Cf. A007318 Pascal's triangle read by rows, A113172.
%K A123315 easy,nonn,tabl,word
%O A123315 1,2
%A A123315 _Jonathan Vos Post_, Nov 08 2006