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 A194229 Partial sums of A057357. 2
 0, 1, 2, 4, 6, 9, 12, 15, 19, 23, 28, 33, 39, 45, 51, 58, 65, 73, 81, 90, 99, 108, 118, 128, 139, 150, 162, 174, 186, 199, 212, 226, 240, 255, 270, 285, 301, 317, 334, 351, 369, 387, 405, 424, 443, 463, 483, 504, 525, 546, 568, 590, 613, 636, 660, 684, 708 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,1,-2,1). FORMULA G.f.: x^2*(1-x+x^2)*(1+x+x^2) / ((1-x)^3*(1+x+x^2+x^3+x^4+x^5+x^6)). - Colin Barker, Jan 09 2016 G.f.: x^2*(1-x^6) / ((1-x)^2*(1-x^2)*(1-x^7)). - Michael Somos, Sep 13 2023 EXAMPLE G.f. = x^2 + 2*x^3 + 4*x^4 + 6*x^5 + 9*x^6 + 12*x^7 + 15*x^8 + ... - Michael Somos, Sep 13 2023 MATHEMATICA r = 3/7; a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]] Table[a[n], {n, 1, 90}] (* A057357 *) s[n_] := Sum[a[k], {k, 1, n}] Table[s[n], {n, 1, 100}] (* A194229 *) Table[Sum[Floor[3*k/7], {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, Nov 03 2017 *) a[ n_] := Floor[(n^2 + n)*3/14]; (* Michael Somos, Sep 13 2023 *) PROG (PARI) concat(0, Vec(x^2*(1-x+x^2)*(1+x+x^2)/((1-x)^3*(1+x+x^2+x^3+x^4 +x^5+x^6)) + O(x^100))) \\ Colin Barker, Jan 09 2016 (PARI) a(n) = sum(k=1, n, 3*k\7); \\ Michel Marcus, Nov 03 2017 (PARI) {a(n) = (n^2+n)*3\14}; /* Michael Somos, Sep 13 2023 */ CROSSREFS Cf. A057357. Sequence in context: A075349 A156024 A234363 * A194201 A194203 A261222 Adjacent sequences: A194226 A194227 A194228 * A194230 A194231 A194232 KEYWORD nonn,easy AUTHOR Clark Kimberling, Aug 19 2011 STATUS approved

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Last modified September 10 02:36 EDT 2024. Contains 375769 sequences. (Running on oeis4.)