A382816 a(n) = number of occurrences of n in A008949.

1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 2

Author

Clark Kimberling, Apr 07 2025

Keywords

• nonn

Comments

Numbers that occur exactly 2 times: (4, 7, 8, 11, 15, 22, 26, 29, 31, 32, 37, 42, 46, 56, 57, 63, 67, 79, 92, 93, 99, 106,...)

Numbers that occur exactly 3 times: (16, 64, 232, 256, 466, 562, 1024, 1486, 2048,...)

The least number that occurs exactly 4 times is 4096.

Examples

			The numbers in A008949 (partial sums of Pascal's triangle) begin thus:
  1
  1    2
  1    3     4
  1    4     7     8
  1    5    11    15    16
  1    6    16    26    31    32
  1    7    22    42    57    63    64
one 2, one 3, two 4's, etc.
		

Crossrefs

Cf. A007318, A008949, A382817.

Programs

Mathematica

t = Flatten[Accumulate/@Table[Binomial[n, i], {n, 0, 200}, {i, 0, n}]]; (* A008949 *)
Flatten[Table[Count[t, n], {n, 2, 200}]]

PARI

row(n) = my(v=vector(n+1, k, binomial(n,k-1))); vector(#v, k, sum(i=1, k, v[i]));
a(n) = sum (i=1, n+1, #select(x->(x==n), row(i))); \\ Michel Marcus, Apr 13 2025