A066353 - OEIS

%I #14 Jul 21 2023 01:43:40

%S 1,3,6,10,15,21,28,38,50,64,80,98,118,140,164,190,220,253,289,328,370,

%T 415,463,514,568,625,685,748,816,888,964,1044,1128,1216,1308,1404,

%U 1504,1608,1716,1828,1944,2064,2188,2318,2453,2593,2738,2888

%N 1 + partial sums of A032378.

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

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

%H G. C. Greubel, <a href="/A066353/b066353.txt">Table of n, a(n) for n = 0..10000</a>

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

%t A032378:= A032378= Table[k*j, {k,15}, {j,k^2+1, k^2+3*k+3}]//Flatten;

%t A066353[n_]:= A066353[n]= 1 +Sum[A032378[[j+1]], {j,0,n-1}];

%t Table[A066353[n], {n,0,100}] (* _G. C. Greubel_, Jul 20 2023 *)

%o (Magma)

%o A032378:=[k*j: j in [(k^2+1)..(k^2+3*k+3)], k in [1..15]];

%o [n eq 0 select 1 else 1+(&+[A032378[j]: j in [1..n]]): n in [0..100]]; // _G. C. Greubel_, Jul 20 2023

%o (SageMath)

%o A032378=flatten([[k*j for j in range((k^2+1),(k^2+3*k+3)+1)] for k in range(1,15)])

%o def A066353(n): return 1 if (n==0) else 1 + sum(A032378[j] for j in range(n))

%o [A066353(n) for n in range(101)] # _G. C. Greubel_, Jul 20 2023

%Y Cf. A032378, A112873.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Dec 22 2001