cp's OEIS Frontend

A111712 Arithmetic mean of the n-th row of triangle mentioned in A111710.

%I A111712 #15 Jul 23 2024 01:00:43
%S A111712 1,3,6,10,16,22,31,39,51,61,76,88,106,120,141,157,181,199,226,246,276,
%T A111712 298,331,355,391,417,456,484,526,556,601,633,681,715,766,802,856,894,
%U A111712 951,991,1051,1093,1156,1200,1266,1312,1381,1429,1501,1551,1626,1678
%N A111712 Arithmetic mean of the n-th row of triangle mentioned in A111710.
%H A111712 Reinhard Zumkeller, <a href="/A111712/b111712.txt">Table of n, a(n) for n = 1..10000</a>
%H A111712 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A111712 a(1)=1, a(2n) = a(2n-1)+2n, a(2n+1)=a(2n)+3n. a(n) = A111711(n)+floor(n/2). - _Franklin T. Adams-Watters_, May 01 2006
%e A111712 a(4) = (8+9+10+13)/4 =10
%t A111712 With[{r = Range[50]}, Accumulate[Join[{1}, Riffle[2*r, 3*r]]]] (* or *)
%t A111712 LinearRecurrence[{1, 2, -2, -1, 1}, {1, 3, 6, 10, 16}, 100] (* _Paolo Xausa_, Feb 09 2024 *)
%o A111712 (Haskell)
%o A111712 a111712 n = a111712_list !! (n-1)
%o A111712 a111712_list = scanl (+) 1 a195013_list
%o A111712 -- _Reinhard Zumkeller_, Apr 06 2015
%Y A111712 Cf. A111710, A111711.
%Y A111712 Partial sums of A195013 prepended with 1.
%K A111712 easy,nonn
%O A111712 1,2
%A A111712 _Amarnath Murthy_, Aug 24 2005
%E A111712 More terms from _Franklin T. Adams-Watters_, May 01 2006