cp's OEIS Frontend

A261016 a(n) = Sum_{k=0..2^n-1} k*A261015(n,k).

%I A261016 #28 Aug 02 2018 15:44:12
%S A261016 1,6,18,46,107,241,535,1178,2569,5546,11859,25156,53058,111379,232966,
%T A261016 486023,1012185,2104729,4370644,9064924,18778766,38856079,80307630,
%U A261016 165790125,341872016,704171185,1448812630,2977673003,6113469501,12538958895,25693167881,52598980642
%N A261016 a(n) = Sum_{k=0..2^n-1} k*A261015(n,k).
%C A261016 The scaled values a(n)/2^n are (to nine decimal places) 0.5000000000, 1.500000000, 2.250000000, 2.875000000, 3.343750000, 3.765625000, 4.179687500, 4.601562500, 5.017578125, 5.416015625, 5.790527344, 6.141601562, 6.476806641, 6.798034668, 7.109558105, 7.416122437, 7.722358704, 8.028903961, 8.336341858, 8.644985199, 8.954413414, 9.264011145, 9.573415518, 9.881861508, 10.18858004, 10.49296834, 10.79449527, 11.09269635, 11.38722431, 11.67781548, 11.96431363, 12.24665452, ...
%H A261016 Alois P. Heinz and Hiroaki Yamanouchi, <a href="/A261016/b261016.txt">Table of n, a(n) for n = 1..58</a> (a(1)-a(36) from Alois P. Heinz)
%t A261016 (* This program is not suitable to compute more than a dozen terms. *)
%t A261016 notVis[bits_] := For[i = 0, True, i++, If[SequencePosition[bits, IntegerDigits[i, 2]] == {}, Return[i]]];
%t A261016 T[n_, k_] := Select[Rest[IntegerDigits[#, 2]] & /@ Range[2^n, 2^(n+1) - 1], notVis[#] == k &] // Length;
%t A261016 a[n_] := Sum[k*T[n, k], {k, 0, 2^n - 1}];
%t A261016 Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 12}] (* _Jean-François Alcover_, Aug 02 2018 *)
%o A261016 (Haskell)
%o A261016 a261016 = sum . zipWith (*) [0..] . a261019_row'
%o A261016 -- _Reinhard Zumkeller_, Aug 18 2015
%Y A261016 Cf. A261019, A261015, A260273.
%K A261016 nonn
%O A261016 1,2
%A A261016 _N. J. A. Sloane_, Aug 16 2015
%E A261016 a(5)-a(16) from _Alois P. Heinz_, Aug 17 2015
%E A261016 a(17)-a(25) from _Reinhard Zumkeller_, Aug 18 2015
%E A261016 a(26)-a(32) from _Alois P. Heinz_, Aug 19 2015