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 A182453 a(n) = 3^n - n*(n-1)/2. 0
 1, 3, 8, 24, 75, 233, 714, 2166, 6533, 19647, 59004, 177092, 531375, 1594245, 4782878, 14348802, 43046601, 129140027, 387420336, 1162261296, 3486784211, 10460352993, 31381059378, 94143178574, 282429536205, 847288609143, 2541865828004, 7625597484636, 22876792454583, 68630377364477, 205891132094214, 617673396283482, 1853020188851345, 5559060566554995 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n>0, r(n)=a(n)/a(n-1) is approximately equal to 3. Average of the sum of r(n) is 3. Except for r(3) = 2.666666666666667, all other r(n)'s are just above zero and r(n) tends to 3 as n tends to infinity. LINKS Index entries for linear recurrences with constant coefficients, signature (6,-12,10,-3). FORMULA G.f.: (1-3*x+2*x^2+2*x^3)/((1-x)^3*(1-3*x)). [Colin Barker, May 07 2012] EXAMPLE For n=6, a(n)=714, a(n-1)=233, r(n)=3.0643776824034334763948497854077. For n=21, a(n)=10460352993, a(n-1)=3486784211, r(n) = 3.0000001032469972946083183924341. CROSSREFS Sequence in context: A281872 A046342 A238977 * A047087 A000958 A148782 Adjacent sequences:  A182450 A182451 A182452 * A182454 A182455 A182456 KEYWORD nonn,easy AUTHOR Aditya Subramanian, Apr 29 2012 EXTENSIONS Edited by N. J. A. Sloane, May 01 2012 STATUS approved

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Last modified January 28 22:30 EST 2022. Contains 350669 sequences. (Running on oeis4.)