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

%I #13 Feb 01 2023 04:57:07

%S 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 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 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 Triangle, (1, 1, 2, 2, 2, ...) in every column.

%C 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 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 First few rows of the triangle:

%e 1;

%e 1, 1;

%e 2, 1, 1;

%e 2, 2, 1, 1;

%e 2, 2, 2, 1, 1;

%e ...

%p A129765 := proc(n,m) if abs(n-m)<2 then 1 ; else 2 ; end if ; end proc:

%p 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 Table[PadLeft[{1,1},n,2],{n,20}]//Flatten (* _Harvey P. Dale_, May 20 2019 *)

%Y Cf. A004277, A002064, A000325, A130197.

%K nonn,tabl,easy

%O 1,4

%A _Gary W. Adamson_, May 16 2007

%E More terms from _R. J. Mathar_, Jun 08 2007