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 A160805 a(n) = (2*n^3 + 9*n^2 + n + 24) / 6. 3
 4, 6, 13, 27, 50, 84, 131, 193, 272, 370, 489, 631, 798, 992, 1215, 1469, 1756, 2078, 2437, 2835, 3274, 3756, 4283, 4857, 5480, 6154, 6881, 7663, 8502, 9400, 10359, 11381, 12468, 13622, 14845, 16139, 17506, 18948, 20467, 22065, 23744, 25506, 27353, 29287 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Arithmetic progression of third order; a(n+1)-a(n) = A008865(n+2); a(n) = A101986(n) + 4. REFERENCES R. Courant, Differential and Integral Calculus Vol. I (Blackie&Son, 1937), ch. I.4, Example 5, p.29. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = (2*n^3 + 9*n^2 + n + 24) / 6. From Wesley Ivan Hurt, Aug 29 2015: (Start) G.f.: (4-10*x+13*x^2-5*x^3)/(x-1)^4. a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4), n>3. (End) MAPLE A160805:=n->(2*n^3+9*n^2+n+24)/6: seq(A160805(n), n=0..80); # Wesley Ivan Hurt, Aug 29 2015 MATHEMATICA Table[(2 n^3 + 9 n^2 + n + 24)/6, {n, 0, 60}] CoefficientList[Series[(4 - 10*x + 13*x^2 - 5*x^3)/(x - 1)^4, {x, 0, 60}], x] (* Wesley Ivan Hurt, Aug 29 2015 *) PROG (MAGMA) [(2*n^3+9*n^2+n+24)/6: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010 (PARI) first(m)=vector(m, i, i--; (2*i^3 + 9*i^2 + i + 24) / 6) \\ Anders HellstrÃ¶m, Aug 29 2015 CROSSREFS Cf. A008865, A101986. Sequence in context: A136391 A105205 A302311 * A246424 A012776 A240198 Adjacent sequences:  A160802 A160803 A160804 * A160806 A160807 A160808 KEYWORD nonn,easy AUTHOR Reinhard Zumkeller, May 26 2009 STATUS approved

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Last modified August 14 18:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)