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A066353
1 + partial sums of A032378.
3
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
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
Sequence in context: A358038 A025706 A025730 * A179653 A117520 A147846
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 22 2001
STATUS
approved