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0, 0, 1, 2, 3, 5, 8, 11, 14, 17, 21, 25, 29, 34, 40, 46, 52, 58, 65, 72, 79, 87, 96, 105, 114, 123, 133, 143, 153, 164, 176, 188, 200, 212, 225, 238, 251, 265, 280, 295, 310, 325, 341, 357, 373, 390, 408, 426, 444, 462, 481, 500, 519, 539, 560, 581, 602
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = 2*a(n-1) - a(n-2) + a(n-8) - 2*a(n-9) + a(n-10) for n > 10.
G.f.: x^3*(1 + x^3 + x^4)/((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x^4)). (End)
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MAPLE
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seq(coeff(series( x^3*(1+x^3+x^4)/((1-x)^2*(1-x^8)) , x, n+1), x, n), n = 1..60); # G. C. Greubel, Jun 10 2020
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MATHEMATICA
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r = 1/4;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}] (* A194220 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194221 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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