A115356 - OEIS

A115356

Matrix (1,x)+(x,x^2) in Riordan array notation.

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

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OFFSET

0,1

COMMENTS

As a flat sequence, with starting offset=1, a(n) = 1 if n is a triangular number (A000217) or twice a square (A001105), otherwise 0. - Antti Karttunen, Jan 19 2025

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..101474; the first 450 rows of the triangle

Wikipedia, Riordan array

Index entries for characteristic functions.

FORMULA

Number triangle T(n, k) = if(n=k, 1, 0) OR if(n=2k+1, 1, 0).

a(n) = A010054(n) + A379480(n). [As a flat sequence with starting offset 1] - Antti Karttunen, Jan 19 2025

EXAMPLE

Triangle begins:

n\k| 0 1 2 3 4 5 6 7 8 9

---+-------------------------------

0 | 1;

1 | 1, 1;

2 | 0, 0, 1;

3 | 0, 1, 0, 1;

4 | 0, 0, 0, 0, 1;

5 | 0, 0, 1, 0, 0, 1;

6 | 0, 0, 0, 0, 0, 0, 1;

7 | 0, 0, 0, 1, 0, 0, 0, 1;

8 | 0, 0, 0, 0, 0, 0, 0, 0, 1;

9 | 0, 0, 0, 0, 1, 0, 0, 0, 0, 1;

(row and column numbering added by Antti Karttunen, Jan 19 2025)

PROG

(PARI)

A115356off1(n) = (ispolygonal(n, 3) || (!(n%2) && issquare(n/2))); \\ (This is one-based)

A115356(n) = A115356off1(1+n); \\ (zero-based) - Antti Karttunen, Jan 19 2025

CROSSREFS

Row sums are A000034. Diagonal sums are A115357. Inverse is A115358.

Cf. A000217, A001105, A010054, A379480.

Cf. also A115359.

Sequence in context: A229894 A256538 A074910 * A115359 A117906 A090678

Adjacent sequences: A115353 A115354 A115355 * A115357 A115358 A115359

KEYWORD

easy,nonn,tabl,changed

AUTHOR

Paul Barry, Jan 21 2006

STATUS

approved

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