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A235794 Triangle read by rows: T(n,k), n>=1, k>=1, in which column k starts with k zeros and then lists the odd numbers interleaved with k zeros, and the first element of column k is in row k(k+1)/2. 10
0, 1, 0, 0, 3, 0, 0, 1, 5, 0, 0, 0, 0, 0, 7, 3, 0, 0, 0, 1, 9, 0, 0, 0, 0, 5, 0, 0, 11, 0, 0, 0, 0, 0, 3, 0, 13, 7, 0, 1, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 9, 5, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 3, 0, 19, 11, 0, 0, 1, 0, 0, 7, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

It appears that the alternating row sums give A120444, the first differences of A004125, i.e., sum_{k=1..A003056(n))} (-1)^(k-1)*T(n,k) = A120444(n).

Row n has length A003056(n) hence the first element of column k is in row A000217(k).

LINKS

Table of n, a(n) for n=1..83.

EXAMPLE

Triangle begins:

0;

1;

0,  0;

3,  0;

0,  1;

5,  0,  0;

0,  0,  0;

7,  3,  0;

0,  0,  1;

9,  0,  0,  0;

0,  5,  0,  0;

11, 0,  0,  0;

0,  0,  3,  0;

13, 7,  0,  1;

0,  0,  0,  0,  0;

15, 0,  0,  0,  0;

0,  9,  5,  0,  0;

17, 0,  0,  0,  0;

0,  0,  0,  3,  0;

19, 11, 0,  0,  1;

0,  0,  7,  0,  0,  0;

21, 0,  0,  0,  0,  0;

0,  13, 0,  0,  0,  0;

23, 0,  0,  5,  0,  0;

...

For n = 14 the 14th row of triangle is 13, 7, 0, 1, and the alternating sum is 13 - 7 + 0 - 1 = 5, the same as A120444(14) = 5.

CROSSREFS

Cf. A000203, A000217, A003056, A004125, A120444, A196020, A211343, A228813, A231345, A231347, A235791, A236104, A236106, A236112.

Sequence in context: A126723 A325846 A325735 * A090030 A293616 A211649

Adjacent sequences:  A235791 A235792 A235793 * A235795 A235796 A235797

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Jan 23 2014

STATUS

approved

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Last modified October 23 14:45 EDT 2019. Contains 328345 sequences. (Running on oeis4.)