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%I #20 Jun 21 2023 15:44:08
%S 1,2,5,8,14,19,28,35,47,56,71,82,100,113,134,149,173,190,217,236,266,
%T 287,320,343,379,404,443,470,512,541,586,617,665,698,749,784,838,875,
%U 932,971,1031,1072,1135,1178,1244,1289,1358,1405,1477,1526,1601,1652
%N Leading column of triangle mentioned in A111710.
%C Also partial sums of A257143. - _Reinhard Zumkeller_, Apr 17 2015
%H Reinhard Zumkeller, <a href="/A111711/b111711.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F a(1)=1, a(2n) = a(2n-1)+2n-1, a(2n+1)=a(2n)+3n; a(n) = A111710(n-1)+1. - _Franklin T. Adams-Watters_, May 01 2006
%F From _Chai Wah Wu_, Mar 05 2021: (Start)
%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 5.
%F G.f.: x*(-x^4 - x^3 - x^2 - x - 1)/((x - 1)^3*(x + 1)^2). (End)
%F a(n) = (10*n*(n-1) + (-1)^n*(1-2*n)+15)/16. - _Eric Simon Jacob_, Jun 11 2022
%t LinearRecurrence[{1,2,-2,-1,1},{1,2,5,8,14},60] (* _Harvey P. Dale_, Jun 21 2023 *)
%o (Haskell)
%o a111711 n = a111711_list !! (n-1)
%o a111711_list = 1 : zipWith (+) a111711_list a080512_list
%o -- _Reinhard Zumkeller_, Apr 17 2015
%Y Cf. A111710, A111712, A080512, A257143.
%K easy,nonn
%O 1,2
%A _Amarnath Murthy_, Aug 24 2005
%E More terms from _Franklin T. Adams-Watters_, May 01 2006
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