

A095802


Upper right triangular matrix T^2, where T(i,j) = (1)^i*(12*i) for 1 <= i <= j.


1



1, 2, 9, 3, 6, 25, 4, 15, 10, 49, 5, 12, 35, 14, 81, 6, 21, 20, 63, 18, 121, 7, 18, 45, 28, 99, 22, 169, 8, 27, 30, 77, 36, 143, 26, 225, 9, 24, 55, 42, 117, 44, 195, 30, 289, 10, 33, 40, 91, 54, 165, 52, 255, 34, 361, 11, 30, 65, 56, 135, 66, 221, 60, 323, 38, 441, 12, 39, 50, 105, 72, 187, 78, 285, 68, 399, 42, 529
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OFFSET

1,2


COMMENTS

Equivalently, (lower left) triangle M^2 = transpose(T)^2. The following description refers to the lower triangular version, but OEIS's "TABL" link displays the values more appropriately as an upper right triangle.  M. F. Hasler, Apr 18 2009
For n rows, use matrices in each row from the sequence 1, 3, 5, 7, ... (filling in with zeros except for the nth row). Let the matrix = M, then square and delete the zeros. For example, the 3row generator would be [1 0 0 / 1 3 0 / 1 3 5] = M. The nonzero elements of M^2 give the first 6 terms of the sequence.


LINKS



FORMULA

Diagonal elements are the odd squares: a(k(k+1)/2)=(2k+1)^2. First element in row k is (1)^k*k.  M. F. Hasler, Apr 18 2009


EXAMPLE

The matrix
[ 1 0 0 0 ...]
[ 1 3 0 0 ...]
[ 1 3 5 0 ...]
[ 1 3 5 7 ...]
squared yields
[ +1 0 0 0 ...]
[ 2 +9 0 0 ...]
[ +3 6 25 0 ...]
[ 4 15 10 49 ...]; the lower left triangle gives this sequence: 1; 2, 9; 3, 6, 25; ...


PROG

(PARI) T=matrix(12, 12, i, j, if(j>=i, (1)^i*(12*i)))^2; concat(vector(#T, i, vecextract(T[, i], 2^i1))) \\ M. F. Hasler, Apr 18 2009


CROSSREFS

Row sums with signs as shown = A002412, Hexagonal pyramidal numbers: (1, 7, 22, 50, 95, ...).


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AUTHOR



EXTENSIONS



STATUS

approved



