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 A194236 Partial sums of A194235. 3
 0, 0, 0, 1, 2, 4, 7, 10, 13, 16, 20, 24, 29, 35, 42, 49, 56, 63, 70, 78, 86, 95, 105, 115, 125, 135, 146, 157, 169, 182, 196, 210, 224, 238, 252, 267, 282, 298, 315, 332, 349, 366, 384, 402, 421, 441, 462, 483, 504, 525, 546, 568, 590, 613, 637, 661, 685 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 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-16) - 2*a(n-17) + a(n-18) for n > 18. G.f.: x*(-x^14 - x^13 - x^12 - x^10 - x^6 - x^5 - x^3)/(x^18 - 2*x^17 + x^16 - x^2 + 2*x - 1). (End) MATHEMATICA r = 1/8; a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]] Table[a[n], {n, 1, 90}] (* A194235 *) s[n_] := Sum[a[k], {k, 1, n}] Table[s[n], {n, 1, 100}] (* A194236 *) PROG (PARI) f(n) = floor(sum(k=1, n, frac(k/8))); a(n) = sum(k=1, n, f(k)); \\ Michel Marcus, Nov 03 2017 CROSSREFS Cf. A194235. Sequence in context: A001195 A295513 A194228 * A127762 A137281 A287420 Adjacent sequences: A194233 A194234 A194235 * A194237 A194238 A194239 KEYWORD nonn AUTHOR Clark Kimberling, Aug 20 2011 STATUS approved

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Last modified September 27 04:27 EDT 2023. Contains 365672 sequences. (Running on oeis4.)