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A115512 Number triangle (1,x)+(x,x^3) expressed in terms of Riordan arrays. 1
1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are periodic {1,2,1}. Diagonal sums are periodic {1,1,1,0}. Inverse is A115513.

LINKS

Table of n, a(n) for n=0..104.

FORMULA

Column k has g.f. x^k+x^(3k+1); Number triangle T(n, k)=if(n=k, 1, 0) OR if(n=3k+1, 1, 0).

EXAMPLE

Triangle begins

1,

1, 1,

0, 0, 1,

0, 0, 0, 1,

0, 1, 0, 0, 1,

0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 1,

0, 0, 1, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

CROSSREFS

Sequence in context: A128190 A128189 A303340 * A115513 A133080 A316917

Adjacent sequences:  A115509 A115510 A115511 * A115513 A115514 A115515

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jan 23 2006

STATUS

approved

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Last modified June 12 13:48 EDT 2021. Contains 344948 sequences. (Running on oeis4.)