A239662 Triangle read by rows: T(n,k), n>=1, k>=1, in which column k lists the numbers A017113 interleaved with k-1 zeros, and the first element of column k is in row k(k+1)/2.

4, 12, 20, 4, 28, 0, 36, 12, 44, 0, 4, 52, 20, 0, 60, 0, 0, 68, 28, 12, 76, 0, 0, 4, 84, 36, 0, 0, 92, 0, 20, 0, 100, 44, 0, 0, 108, 0, 0, 12, 116, 52, 28, 0, 4, 124, 0, 0, 0, 0, 132, 60, 0, 0, 0, 140, 0, 36, 20, 0, 148, 68, 0, 0, 0, 156, 0, 0, 0, 12, 164, 76, 44, 0, 0, 4, 172, 0, 0, 28, 0, 0, 180, 84, 0, 0, 0, 0, 188, 0, 52, 0, 0, 0

Offset

1,1

Comments

Gives an identity for A239050. Alternating sum of row n equals A239050(n), i.e., Sum_{k=1..A003056(n)} (-1)^(k-1)*T(n,k) = 4*A000203(n) = 2*A074400(n) = A239050(n).

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

Note that if T(n,k) = 12 then T(n+1,k+1) = 4, the first element of the column k+1.

The number of positive terms in row n is A001227(n).

For more information see A196020.

Column 1 is A017113. - Omar E. Pol, Apr 17 2016

Links

Table of n, a(n) for n=1..94.

Formula

T(n,k) = 2*A236106(n,k) = 4*A196020(n,k).

Example

Triangle begins:
  4;
  12;
  20,   4;
  28,   0;
  36,  12;
  44,   0,  4;
  52,  20,  0;
  60,   0,  0;
  68,  28, 12;
  76,   0,  0,  4;
  84,  36,  0,  0;
  92,   0, 20,  0;
  100, 44,  0,  0;
  108,  0,  0, 12;
  116, 52, 28,  0,  4;
  124,  0,  0,  0,  0;
  132, 60,  0,  0,  0;
  140,  0, 36, 20,  0;
  148, 68,  0,  0,  0;
  156,  0,  0,  0, 12;
  164, 76, 44,  0,  0,  4;
  172,  0,  0, 28,  0,  0;
  180, 84,  0,  0,  0,  0;
  188,  0, 52,  0,  0,  0;
  ...
For n = 9, the 9th row of triangle is [68, 28, 12], therefore the alternating row sum is 68 - 28 + 12 = 52. On the other hand we have that 4*A000203(9) = 2*A074400(9) = A239050(9) = 4*13 = 2*26 = 52, equaling the alternating sum of the 9th row of the triangle.

Crossrefs

Cf. A000203, A000217, A003056, A017113, A074400, A196020, A211343, A235791, A236104, A236106, A236112, A237048, A237591, A239050, A239446.

Sequence in context: A240762 A319259 A050021 * A321769 A133096 A309085

Adjacent sequences: A239659 A239660 A239661 * A239663 A239664 A239665

Keyword

nonn,tabf

Author

Omar E. Pol, Mar 30 2014

Status

approved