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

0,2

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

Formula

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A032378, A112873.

Sequence in context: A358038 A025706 A025730 * A179653 A117520 A147846

Adjacent sequences: A066350 A066351 A066352 * A066354 A066355 A066356

Keyword

nonn

Author

N. J. A. Sloane, Dec 22 2001

Status

approved