A318872 Partial sums of A316156.

1, 3, 6, 12, 19, 27, 36, 49, 64, 81, 99, 118, 138, 169, 201, 240, 280, 323, 378, 437, 500, 564, 629, 695, 762, 830, 899, 969, 1040, 1112, 1185, 1271, 1376, 1482, 1589, 1697, 1806, 1916, 2027, 2145, 2280, 2416, 2553, 2709, 2866, 3024, 3183, 3343, 3504, 3666, 3829, 3993, 4158, 4324, 4491, 4675, 4860, 5046, 5233, 5428

Offset: 1

Author

Antti Karttunen, Sep 16 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A316156.

Programs

PARI

up_to = 10000;
povisin(v,n) = { forstep(j=n,1,-1, if(v[j] == n, return(j))); (0); }; \\ Here: povisin = position_of_n_in_strictly_increasing_v
A318872list(up_to) = { my(v316156 = vector(up_to), v318872 = vector(up_to), k, s); v316156[1] = v318872[1] = 1; for(n=2, up_to, k = 1+v316156[n-1]; if(povisin(v316156, n-1), s = v318872[n-1]; while((s+k)%(n-1), k++)); v316156[n] = k; v318872[n] = v318872[n-1] + v316156[n]); (v318872); };
v318872 = A318872list(up_to);
A318872(n) = v318872[n];

Formula

a(n) = Sum_{k=1..n} A316156(k).