cp's OEIS Frontend

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

%I A382816 #13 Apr 13 2025 11:47:20
%S A382816 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,
%T A382816 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,
%U A382816 1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1
%N A382816 a(n) = number of occurrences of n in A008949.
%C A382816 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,...)
%C A382816 Numbers that occur exactly 3 times: (16, 64, 232, 256, 466, 562, 1024, 1486, 2048,...)
%C A382816 The least number that occurs exactly 4 times is 4096.
%e A382816 The numbers in A008949 (partial sums of Pascal's triangle) begin thus:
%e A382816   1
%e A382816   1    2
%e A382816   1    3     4
%e A382816   1    4     7     8
%e A382816   1    5    11    15    16
%e A382816   1    6    16    26    31    32
%e A382816   1    7    22    42    57    63    64
%e A382816 one 2, one 3, two 4's, etc.
%t A382816 t = Flatten[Accumulate/@Table[Binomial[n, i], {n, 0, 200}, {i, 0, n}]]; (* A008949 *)
%t A382816 Flatten[Table[Count[t, n], {n, 2, 200}]]
%o A382816 (PARI) row(n) = my(v=vector(n+1, k, binomial(n,k-1))); vector(#v, k, sum(i=1, k, v[i]));
%o A382816 a(n) = sum (i=1, n+1, #select(x->(x==n), row(i))); \\ _Michel Marcus_, Apr 13 2025
%Y A382816 Cf. A007318, A008949, A382817.
%K A382816 nonn
%O A382816 2,3
%A A382816 _Clark Kimberling_, Apr 07 2025