A135471 a(n) = Sum{i=1..n} ( i*2^(i-1) ) - ( A002024(n)*(A002024(n)+1)/2 - n ) * 2^(A002024(n)-1).

1, 3, 17, 41, 125, 321, 745, 1777, 4089, 9217, 20417, 45009, 98273, 212977, 458753, 982881, 2097025, 4456353, 9437121, 19922913, 41943041, 88080001, 184549057, 385875713, 805306177, 1677721473, 3489660865, 7247757313, 15032384641, 31138512129, 64424508801

Offset

1,2

Comments

At one time this expression was proposed (erroneously) as a formula for A007664.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Mathematica

f[n_] := Floor[Sqrt[2*n] + 1/2]; a[n_] := Sum[ i*2^(i - 1), {i, 1, n}] - (f[n]*(f[n] + 1)/2 - n)*2^(f[n] - 1); Table[a[n], {n, 1, 25}] (* G. C. Greubel, Oct 14 2016 *)

Crossrefs

Cf. A007664.

Sequence in context: A146821 A181981 A089637 * A322755 A226492 A092347

Adjacent sequences: A135468 A135469 A135470 * A135472 A135473 A135474

Keyword

nonn

Author

N. J. A. Sloane, Feb 08 2008

Status

approved