A253903 The characteristic function of square pyramidal numbers.

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

Offset

0

Comments

The n-th 1 is followed by n^2 - 1 zeros.

Run lengths of zeros gives A005563. - Jeremy Gardiner, Jan 14 2018

Square pyramidal numbers are of the form m(m+1)(2m+1)/6.

As pyramid(m) = m(m+1)(2m+1)/6 = m*(m+1/2)*(m+1)/3, (3 * pyramid(m))^(1/3) is slightly less than m + 1/2. - David A. Corneth, Oct 14 2018

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Index entries for characteristic functions

Mathematica

Flatten[Table[Join[{1}, PadRight[{}, n^2-1, 0]], {n, 10}]] (* Harvey P. Dale, Mar 05 2015 *)

Prog

(PARI) lista(nn) = {id = 0; while (id <= nn, print1(1, ", "); id++; for (k=1, id^2-1, print1(0, ", "); ); ); } \\ Michel Marcus, Feb 20 2015
(PARI) a(n) = {if (n <= 1, return (1)); my(s = 1, k = 2); while (s < n, s += k^2; k++); (s == n); } \\ Michel Marcus, Oct 14 2018
(PARI) a(n) = my(m = sqrtnint(3*n, 3)); n==m*(m+1)*(2*m+1)/6 \\ David A. Corneth, Oct 14 2018

Crossrefs

Cf. A000330 (square pyramidal numbers), A282173.

Sequence in context: A359456 A012245 A256436 * A255849 A185059 A179776

Adjacent sequences: A253900 A253901 A253902 * A253904 A253905 A253906

Keyword

nonn

Author

Mikael Aaltonen, Jan 18 2015

Status

approved