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%I #23 Sep 08 2022 08:45:02
%S 1,0,0,1,3,6,9,13,18,24,31,39,47,56,66,77,89,102,115,129,144,160,177,
%T 195,213,232,252,273,295,318,341,365,390,416,443,471,499,528,558,589,
%U 621,654,687,721,756,792,829,867,905,944,984,1025,1067
%N a(n) = round(n*(5*n - 14)/12) + 1.
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 122, see #19 (2), I(n).
%H Harry J. Smith, <a href="/A059293/b059293.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,1,-2,1).
%F From _Chai Wah Wu_, Jun 20 2020: (Start)
%F a(n) = 2*a(n-1) - a(n-2) + a(n-6) - 2*a(n-7) + a(n-8) for n > 7.
%F G.f.: (-3*x^7 + x^6 - x^5 - x^4 - x^3 - x^2 + 2*x - 1)/( (x+1)*(x^2+x+1)*(x^2-x+1)*(x-1)^3). (End)
%t Table[Round[n*(5*n - 14)/12], {n, 0, 10}] + 1 (* _G. C. Greubel_, Jan 04 2017 *)
%t LinearRecurrence[{2,-1,0,0,0,1,-2,1},{1,0,0,1,3,6,9,13},60] (* _Harvey P. Dale_, Mar 06 2022 *)
%o (PARI) { default(realprecision, 100); for (n = 0, 1000, write("b059293.txt", n, " ", round(n*(5*n - 14)/12) + 1); ) } \\ _Harry J. Smith_, Jun 25 2009
%o (Magma) [Round(n*(5*n-14)/12)+1: n in [0..60]]; // _Vincenzo Librandi_, Jan 05 2017
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_, Jan 25 2001
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