A229788 6*2^n - n^2 - 5*n - 6.

0, 0, 4, 18, 54, 136, 312, 678, 1426, 2940, 5988, 12106, 24366, 48912, 98032, 196302, 392874, 786052, 1572444, 3145266, 6290950, 12582360, 25165224, 50330998, 100662594, 201325836, 402652372, 805305498, 1610611806, 3221224480, 6442449888

Offset

0,3

Comments

Sum_{i = 1 .. n} (i^2 + i - 2)/2^i = a(n)/2^n so we see that the sum approaches 6 as n gets large.

Links

Table of n, a(n) for n=0..30.

Formula

O.g.f.: (4 - 2x)*x^2/((1 - x)^3*(1 - 2x)).

Mathematica

RecurrenceTable[{a[n] == 2a[n - 1] + n^2 + n - 2, a[1] == 0}, a, {n, 1, 25}]
Table[6*2^n - n^2 - 5*n - 6, {n, 0, 30}] (* T. D. Noe, Oct 01 2013 *)

Crossrefs

Sequence in context: A020644 A182031 A212250 * A242206 A181411 A238915

Adjacent sequences: A229785 A229786 A229787 * A229789 A229790 A229791

Keyword

nonn,easy

Author

Geoffrey Critzer, Sep 29 2013

Status

approved