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 A194224 Partial sums of A194223. 3
 0, 0, 1, 2, 4, 6, 8, 11, 14, 18, 23, 28, 33, 38, 44, 50, 57, 64, 71, 79, 87, 96, 106, 116, 126, 136, 147, 158, 170, 182, 194, 207, 220, 234, 249, 264, 279, 294, 310, 326, 343, 360, 377, 395, 413, 432, 452, 472, 492, 512, 533, 554, 576, 598, 620, 643, 666 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 FORMULA From Chai Wah Wu, Jun 10 2020: (Start) a(n) = 2*a(n-1) - a(n-2) + a(n-12) - 2*a(n-13) + a(n-14) for n > 14. G.f.: x*(-x^10 - x^9 - x^7 - x^4 - x^2)/(x^14 - 2*x^13 + x^12 - x^2 + 2*x - 1). (End) MATHEMATICA r = 1/6; a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]] Table[a[n], {n, 1, 90}] (* A194223 *) s[n_] := Sum[a[k], {k, 1, n}] Table[s[n], {n, 1, 100}] (* A194224 *) PROG (PARI) for(n=1, 50, print1(sum(j=1, n, floor(sum(k=1, j, frac(k/6)))), ", ")) \\ G. C. Greubel, Oct 29 2017 CROSSREFS Cf. A194223. Sequence in context: A194162 A084627 A321531 * A194252 A205727 A213609 Adjacent sequences: A194221 A194222 A194223 * A194225 A194226 A194227 KEYWORD nonn AUTHOR Clark Kimberling, Aug 19 2011 STATUS approved

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Last modified June 3 02:49 EDT 2023. Contains 363102 sequences. (Running on oeis4.)