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A143156 Triangle read by rows, T(n,k) = sum {j=k..n} A001511(j); = A000012 * (A001511 * 0^(n-k)) * A000012; 1<=k<=n. 1
1, 3, 2, 4, 3, 1, 7, 6, 4, 3, 8, 7, 5, 4, 1, 10, 9, 7, 6, 3, 2, 11, 10, 8, 7, 4, 3, 1, 15, 14, 12, 11, 8, 7, 5, 4, 16, 15, 13, 12, 9, 8, 6, 5, 1, 18, 17, 15, 14, 11, 10, 8, 7, 3, 2, 19, 18, 16, 15, 12, 11, 9, 8, 4, 3, 1, 22, 21, 19, 18, 15, 14, 12, 11, 7, 6, 4, 3 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums = A143157: (1, 5, 8, 20, 25, 37, 44,...).

Left border = A005187: (1, 3, 4, 7, 8, 10, 11,...).

Right border = ruler sequence, A001511: (1, 2, 1, 3, 1, 2, 1, 4,...).

LINKS

Table of n, a(n) for n=1..78.

FORMULA

Triangle read by rows, T(n,k) = sum {j=k..n} A001511(j); = A000012 * (A001511 * 0^(n-k)) * A000012; 1<=k<=n. A001511 = the ruler sequence, (1, 2, 1, 3, 1, 2, 1, 4,...).

EXAMPLE

First few rows of the triangle =

1;

3, 2;

4, 3, 1;

7, 6, 4, 3;

8, 7, 5, 4, 1;

10, 9, 7, 6, 3, 2;

11, 10, 8, 7, 4, 3, 1;

...

Row 6 = (10, 9, 7, 6, 3, 2) = partial sums of the first 6 terms of the ruler sequence, starting from the right: (1, 2, 1, 3, 1, 2,...).

CROSSREFS

Cf. A001511, A000012, A091512, A005187.

Sequence in context: A013633 A016559 A104566 * A227471 A101403 A025509

Adjacent sequences:  A143153 A143154 A143155 * A143157 A143158 A143159

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jul 27 2008

STATUS

approved

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Last modified February 27 17:20 EST 2020. Contains 332307 sequences. (Running on oeis4.)