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

1, 6, 18, 46, 107, 241, 535, 1178, 2569, 5546, 11859, 25156, 53058, 111379, 232966, 486023, 1012185, 2104729, 4370644, 9064924, 18778766, 38856079, 80307630, 165790125, 341872016, 704171185, 1448812630, 2977673003, 6113469501, 12538958895, 25693167881, 52598980642

Offset

1,2

Comments

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, ...

Links

Alois P. Heinz and Hiroaki Yamanouchi, Table of n, a(n) for n = 1..58 (a(1)-a(36) from Alois P. Heinz)

Mathematica

(* This program is not suitable to compute more than a dozen terms. *)
notVis[bits_] := For[i = 0, True, i++, If[SequencePosition[bits, IntegerDigits[i, 2]] == {}, Return[i]]];
T[n_, k_] := Select[Rest[IntegerDigits[#, 2]] & /@ Range[2^n, 2^(n+1) - 1], notVis[#] == k &] // Length;
a[n_] := Sum[k*T[n, k], {k, 0, 2^n - 1}];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 12}] (* Jean-François Alcover, Aug 02 2018 *)

Prog

(Haskell)
a261016 = sum . zipWith (*) [0..] . a261019_row'
-- Reinhard Zumkeller, Aug 18 2015

Crossrefs

Cf. A261019, A261015, A260273.

Sequence in context: A305031 A031128 A304161 * A328890 A188379 A299268

Adjacent sequences: A261013 A261014 A261015 * A261017 A261018 A261019

Keyword

nonn

Author

N. J. A. Sloane, Aug 16 2015

Extensions

a(5)-a(16) from Alois P. Heinz, Aug 17 2015

a(17)-a(25) from Reinhard Zumkeller, Aug 18 2015

a(26)-a(32) from Alois P. Heinz, Aug 19 2015

Status

approved