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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 12 10:47 EDT 2024. Contains 375850 sequences. (Running on oeis4.)