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Triangle by columns: A013610 signed and interleaved with zeros.
1

%I #10 Mar 30 2024 23:09:17

%S 1,0,3,-1,0,9,0,-6,0,27,1,0,-27,0,81,0,9,0,-108,0,243,-1,0,54,0,-405,

%T 0,729,0,-12,0,270,0,-1458,0,2187

%N Triangle by columns: A013610 signed and interleaved with zeros.

%C Row sums = even-indexed Fibonacci numbers, A001906: (1, 3, 8, 21, 55, ...) such that the sum of n-th row terms = F(2n). Example: sum of nonzero terms of row 4 = (-6 + 27) = 21 = F(8).

%F The triangle starts with A013610, then by columns sign (+, -, +, ...) and interleave with zeros.

%e First few rows of the triangle:

%e 1;

%e 0, 3;

%e -1, 0, 9;

%e 0, -6, 0, 27;

%e 1, 0, -27, 0, 81;

%e 0, 9, 0, -108, 0, 243;

%e -1, 0, 54, 0, -405, 0, 729;

%e ...

%Y Cf. A013610, A001906.

%K tabl,sign

%O 1,3

%A _Gary W. Adamson_, Dec 02 2007