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A114212 Generalized Gould sequence. 1
1, 2, 3, 4, 4, 4, 6, 8, 6, 4, 6, 8, 8, 8, 12, 16, 10, 4, 6, 8, 8, 8, 12, 16, 12, 8, 12, 16, 16, 16, 24, 32, 18, 4, 6, 8, 8, 8, 12, 16, 12, 8, 12, 16, 16, 16, 24, 32, 20, 8, 12, 16, 16, 16, 24, 32, 24, 16, 24, 32, 32, 32, 48, 64, 34, 4, 6, 8, 8, 8, 12, 16, 12, 8, 12, 16, 16, 16, 24, 32, 20, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of A114213.

LINKS

Table of n, a(n) for n=0..81.

Jeffrey Shallit, Lukas Spiegelhofer, Continuants, run lengths, and Barry's modified Pascal triangle, arXiv:1710.06203 [math.CO], 2017.

FORMULA

a(n) = Sum_{k=0..n} (Sum_{j=0..n-k} C(k, j)*C(n-k, j)*(1 + (-1)^k)/2 mod 2);

a(n) = A001316(n) + A001316((n-2)/2)*(1 + (-1)^n)/2.

EXAMPLE

From Omar E. Pol, Jun 09 2009: (Start)

Triangle begins:

1;

2,3;

4,4,4,6;

8,6,4,6,8,8,8,12;

16,10,4,6,8,8,8,12,16,12,8,12,16,16,16,24;

32,18,4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,20,8,12,16,16,16,24,32,24,...

Also, we can write the initial term followed by a triangle:

1;

2;

3,4;

4,4,6,8;

6,4,6,8,8,8,12,16;

10,4,6,8,8,8,12,16,12,8,12,16,16,16,24,32;

18,4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,20,8,12,16,16,16,24,32,24,16,...

Also, we can write first two terms followed by a triangle:

1;

2;

3;

4,4;

4,6,8,6;

4,6,8,8,8,12,16,10;

4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,18;

4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,20,8,12,16,16,16,24,32,24,16,24,32,...

(End)

CROSSREFS

Cf. A000079. [Omar E. Pol, Jun 09 2009]

Sequence in context: A221917 A131798 A206925 * A108355 A057951 A076410

Adjacent sequences:  A114209 A114210 A114211 * A114213 A114214 A114215

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 17 2005

STATUS

approved

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Last modified October 23 14:22 EDT 2019. Contains 328345 sequences. (Running on oeis4.)