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A179901 Triangle read by rows, antidiagonals of an array generated from (1, r, r, r, ...) convolved with (1, 0, r, r, r, ...).

%I A179901 #9 Jan 03 2021 01:01:25
%S A179901 1,1,1,1,2,2,1,3,4,3,1,4,6,8,4,1,5,8,15,12,5,1,6,10,24,24,16,6,1,7,12,
%T A179901 35,40,33,20,7,1,8,14,48,60,56,42,24,8,1,9,16,63,84,85,70,51,28,9,1,
%U A179901 10,18,80,112,120,110,88,60,32,10,1,11,20,99,144,161,156,135,104,69,36,11
%N A179901 Triangle read by rows, antidiagonals of an array generated from (1, r, r, r, ...) convolved with (1, 0, r, r, r, ...).
%C A179901 Row sums = A179902: (1, 2, 5, 11, 23, 46, 87, 155, ...).
%F A179901 Triangle read by rows, antidiagonals of an array generated from (1, r, r, r, ...) convolved with (1, 0, r, r, r, ...), such that the r-th row of the array = (1, r, 2*r, ...) then for n > 3, a(n) = r^2 + a(n-1).
%e A179901 First few rows of the array:
%e A179901 .
%e A179901 1,.1,..2,...3,...4,...5,...6,...7,....8,...
%e A179901 1,.2,..4,...8,..12,..16...20,..24,...28,... = A019442
%e A179901 1,.3,..6,..15,..24,..33,..42,..51,...60,... = A179805
%e A179901 1,.4,..8,..24,..40,..56,..70,..88,..104,...
%e A179901 .
%e A179901 Example: row 4 = (1, 4, 8, 24, ...) = (1, 4, 4, 4, ...) * (1, 0, 4, 4, 4, ...) = (1, r, 2*r, (2*r + r^2), ...).
%e A179901 .
%e A179901 First few rows of the triangle:
%e A179901 .
%e A179901 1,
%e A179901 1, 1;
%e A179901 1, 2, 2;
%e A179901 1, 3, 4, 3;
%e A179901 1, 4, 6, 8, 4;
%e A179901 1, 5, 8, 15, 12, 5;
%e A179901 1, 6, 10, 24, 24, 16, 6;
%e A179901 1, 7, 12, 35, 40, 33, 20, 7;
%e A179901 1, 8, 14, 48, 60, 56, 42, 24, 8;
%e A179901 1, 9, 16, 63, 84, 85, 70, 51, 28, 9;
%e A179901 1, 10, 18, 80, 112, 120, 110, 88, 60, 32, 10;
%e A179901 1, 11, 20, 99, 144, 161, 156, 135, 104, 69, 36, 11;
%e A179901 1, 12, 22, 120, 180, 208, 210, 192, 160, 120, 78, 40, 12;
%e A179901 1, 13, 24, 143, 220, 261, 272, 259, 228, 185, 136, 87, 44, 13;
%e A179901 ...
%Y A179901 Cf. A019442, A179805
%K A179901 nonn,tabl
%O A179901 1,5
%A A179901 _Gary W. Adamson_, Jul 31 2010