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 A024305 a(n) = 2*(n+1) + 3*n + ... + (k+1)*(n+2-k), where k = floor((n+1)/2). 6
 4, 6, 17, 22, 43, 52, 86, 100, 150, 170, 239, 266, 357, 392, 508, 552, 696, 750, 925, 990, 1199, 1276, 1522, 1612, 1898, 2002, 2331, 2450, 2825, 2960, 3384, 3536, 4012, 4182, 4713, 4902, 5491, 5700, 6350, 6580, 7294, 7546, 8327, 8602, 9453, 9752, 10676, 11000, 12000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1). FORMULA From Vladeta Jovovic, Jan 01 2003: (Start) a(n) = (1/48)*(4*n^3 + (3*(-1)^(n+1) + 39)*n^2 + (18*(-1)^(n+1) + 74)*n + 27*(-1)^(n+1) + 27). a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7). G.f.: x*(4 + 2*x - x^2 - x^3)/((1+x)^3*(1-x)^4). (End) a(n) = Sum_{i=1..ceiling(n/2)} (i+1)*(n-i+2) = ceiling(n/2)*(-2*ceiling(n/2)^2 + 3n*ceiling(n/2) + 9*n + 14)/6. - Wesley Ivan Hurt, Sep 20 2013 E.g.f.: (1/24)*( x*(69 + 24*x + 2*x^2)*cosh(x) + (27 + 48*x + 27*x^2 + 2*x^3)*sinh(x) ). - G. C. Greubel, Jul 12 2022 MAPLE seq(sum((i+1)*(k-i+2), i=1..ceil(k/2)), k=1..70); # Wesley Ivan Hurt, Sep 20 2013 MATHEMATICA Table[Ceiling[n/2]*(-2*Ceiling[n/2]^2+3n*Ceiling[n/2]+9n+14)/6, {n, 100}] (* Wesley Ivan Hurt, Sep 20 2013 *) PROG (Magma) b:= func< n | (1-(-1)^n)/2 >; [(2*n^3 + 3*(6 +b(n))*n^2 + 2*(14 +9*b(n))*n + 27*b(n))/24 : n in [1..50]] // G. C. Greubel, Jul 12 2022 (SageMath) def b(n): return (1-(-1)^n)/2 [(2*n^3 + 3*(6 +b(n))*n^2 + 2*(14 +9*b(n))*n + 27*b(n))/24 for n in (1..50)] # G. C. Greubel, Jul 12 2022 CROSSREFS Bisection: 2*A051925(n). Cf. A024854, A023855, A023856, A023857, A024868. Sequence in context: A226634 A105271 A343758 * A342231 A320245 A337208 Adjacent sequences: A024302 A024303 A024304 * A024306 A024307 A024308 KEYWORD nonn AUTHOR Clark Kimberling EXTENSIONS Name simplified by Jon E. Schoenfield, Jun 12 2019 STATUS approved

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Last modified December 2 21:06 EST 2023. Contains 367526 sequences. (Running on oeis4.)