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 A227582 Exapansion of (2+3*x+2*x^2+2*x^3+3*x^4+x^5-x^6)/(1-2*x+x^2-x^5+2*x^6-x^7). 2
 2, 7, 14, 23, 35, 50, 67, 86, 107, 131, 158, 187, 218, 251, 287, 326, 367, 410, 455, 503, 554, 607, 662, 719, 779, 842, 907, 974, 1043, 1115, 1190, 1267, 1346, 1427, 1511, 1598, 1687, 1778, 1871, 1967, 2066, 2167, 2270, 2375, 2483, 2594, 2707, 2822, 2939 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS At A227581, it is conjectured that a(n) = floor[1/(2*H(n) + H(n^2 + n - 1) - g], where H denotes harmonic number and g denotes the Euler-Mascheroni constant. LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1) FORMULA a(n) = 2*a(n-1) -a(n-2) +a(n-5) -2*a(n-6) +a(n-7). G.f.: (1+x)*(2+x+x^2+x^3+2*x^4-x^5)/((1-x)^3*(1+x+x^2+x^3+x^4)). MATHEMATICA z = 200; a[1] = 2; a[2] = 7; a[3] = 14; a[4] = 23; a[5] = 35; a[6] = 50; a[7] = 67; a[8] = 86; a[n_] := a[n] = 2*a[n - 1] - a[n - 2] + a[n - 5] - 2*a[n - 6] + a[n - 7]; t = Table[a[n], {n, 1, z}]  (* A277582 *) h[n_] := h[n] = HarmonicNumber[n]; t1 = N[Table[2 h[n] - h[n^2 + n - 1] - EulerGamma, {n, 1, z}]]; Floor[1/t1];  (* conjectured A277582 *) CoefficientList[Series[(1+x)*(2+x+x^2+x^3+2*x^4-x^5)/((1-x)^3*(1+x+x^2+ x^3+x^4)), {x, 0, 50}], x]] (* G. C. Greubel, Aug 04 2018 *) PROG (PARI) x='x+O('x^50); Vec((1+x)*(2+x+x^2+x^3+2*x^4-x^5)/((1-x)^3*(1+x + x^2+x^3+x^4))) \\ G. C. Greubel, Aug 04 2018 (MAGMA) m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x)*(2+x+x^2+x^3+2*x^4-x^5)/((1-x)^3*(1+x+x^2+x^3+x^4)))); // G. C. Greubel, Aug 04 2018 CROSSREFS Cf. A227581. Sequence in context: A087324 A261246 A008865 * A249852 A018392 A051640 Adjacent sequences:  A227579 A227580 A227581 * A227583 A227584 A227585 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jul 17 2013 STATUS approved

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Last modified September 18 11:42 EDT 2018. Contains 315130 sequences. (Running on oeis4.)