A066353 1 + partial sums of A032378.

1, 3, 6, 10, 15, 21, 28, 38, 50, 64, 80, 98, 118, 140, 164, 190, 220, 253, 289, 328, 370, 415, 463, 514, 568, 625, 685, 748, 816, 888, 964, 1044, 1128, 1216, 1308, 1404, 1504, 1608, 1716, 1828, 1944, 2064, 2188, 2318, 2453, 2593, 2738, 2888

Offset: 0

Author

N. J. A. Sloane, Dec 22 2001

Keywords

• nonn

Comments

A032378 has been inspired by the Concrete Mathematics Casino problem (see reference).

References

• R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. 2nd Edition. Addison-Wesley, Reading, MA, 1994. Section 3.2, p74-76.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A032378, A112873.

Programs

Magma

A032378:=[k*j: j in [(k^2+1)..(k^2+3*k+3)], k in [1..15]];
[n eq 0 select 1 else 1+(&+[A032378[j]: j in [1..n]]): n in [0..100]]; // G. C. Greubel, Jul 20 2023

Mathematica

A032378:= A032378= Table[k*j, {k,15}, {j,k^2+1, k^2+3*k+3}]//Flatten;
A066353[n_]:= A066353[n]= 1 +Sum[A032378[[j+1]], {j,0,n-1}];
Table[A066353[n], {n,0,100}] (* G. C. Greubel, Jul 20 2023 *)
Accumulate[Join[{1},Select[Range[300],!IntegerQ[Surd[#,3]]&&Divisible[#,Floor[Surd[#,3]]]&]]] (* Harvey P. Dale, Jan 25 2025 *)

SageMath

A032378=flatten([[k*j for j in range((k^2+1),(k^2+3*k+3)+1)] for k in range(1,15)])
def A066353(n): return 1 if (n==0) else 1 + sum(A032378[j] for j in range(n))
[A066353(n) for n in range(101)] # G. C. Greubel, Jul 20 2023

Formula

a(n) = 1 if n = 0, otherwise a(n) = A112873(n) = Sum_{j=1..n} A032378(j).