cp's OEIS Frontend

A129765 Triangle, (1, 1, 2, 2, 2, ...) in every column.

%I A129765 #13 Feb 01 2023 04:57:07
%S A129765 1,1,1,2,1,1,2,2,1,1,2,2,2,1,1,2,2,2,2,1,1,2,2,2,2,2,1,1,2,2,2,2,2,2,
%T A129765 1,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,2,2,
%U A129765 2,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,2,2,2,1,1
%N A129765 Triangle, (1, 1, 2, 2, 2, ...) in every column.
%C A129765 Row sums = A004277, (1, 2, 4, 6, 8, 10, ...). Binomial transform of (1, 1, 2, 2, 2, ...) = A000325, starting (1, 2, 5, 12, 27, 58, ...). Binomial transform of A130196 = A130197, a triangle with row sums = the Cullen numbers, A002064.
%F A129765 Triangle, (1, 1, 2, 2, 2, ...) in every column. By rows, (1; 1, 1; 2, 1, 1; ...), continuing with (n-2) 2's followed by two 1's. Inverse of A000012 as an infinite lower triangular matrix (all 1's and the rest zeros), signed by columns: (+ - - + + - -, ...).
%e A129765 First few rows of the triangle:
%e A129765   1;
%e A129765   1, 1;
%e A129765   2, 1, 1;
%e A129765   2, 2, 1, 1;
%e A129765   2, 2, 2, 1, 1;
%e A129765   ...
%p A129765 A129765 := proc(n,m) if abs(n-m)<2 then 1 ; else 2 ; end if ; end proc:
%p A129765 for n from 1 to 18 do for m from 1 to n do printf("%d,", A129765(n,m)) ; od ; od ; # _R. J. Mathar_, Jun 08 2007
%t A129765 Table[PadLeft[{1,1},n,2],{n,20}]//Flatten (* _Harvey P. Dale_, May 20 2019 *)
%Y A129765 Cf. A004277, A002064, A000325, A130197.
%K A129765 nonn,tabl,easy
%O A129765 1,4
%A A129765 _Gary W. Adamson_, May 16 2007
%E A129765 More terms from _R. J. Mathar_, Jun 08 2007