A145654 Partial sums of A000918, starting from index 1.

0, 2, 8, 22, 52, 114, 240, 494, 1004, 2026, 4072, 8166, 16356, 32738, 65504, 131038, 262108, 524250, 1048536, 2097110, 4194260, 8388562, 16777168, 33554382, 67108812, 134217674, 268435400, 536870854, 1073741764, 2147483586

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

a(n) = Sum_{i=1..n} A000918(i).

a(n+1) - a(n) = A000918(n+1).

a(n) = A005803(n+1). - R. J. Mathar, Oct 21 2008

From Colin Barker, Jan 11 2012: (Start)

a(n) = 2*(-1 + 2^n - n).

G.f.: 2*x^2/((1-x)^2*(1-2*x)). (End)

a(n+1) = A121173(2*n). - Reinhard Zumkeller, Nov 06 2013

a(n) = Sum_{i=1..n-1} (n-i)*2^i with a(1)=0. - Bruno Berselli, Feb 10 2014

a(n) = 2 * A000295(n). - Alois P. Heinz, May 28 2018

Example

For n=7, a(7) = 6*2 + 5*2^2 + 4*2^3 + 3*2^4 + 2*2^5 + 1*2^6 = 240. - Bruno Berselli, Feb 10 2014
From Bruno Berselli, Jul 17 2018: (Start)
Row sums of the triangle:
   0   ......................................    0
   1,  1   ..................................    2
   3,  2,  3   ..............................    8
   6,  5,  5,  6   ..........................   22
  10, 11, 10, 11, 10   ......................   52
  15, 21, 21, 21, 21, 15   ..................  114
  21, 36, 42, 42, 42, 36, 21   ..............  240
  28, 57, 78, 84, 84, 78, 57, 28   ..........  494, etc.
(End)

Mathematica

Accumulate[2^Range[30] - 2] (* or *) LinearRecurrence[{4, -5, 2}, {0, 2, 8}, 30] (* Harvey P. Dale, Jul 15 2017 *)

Prog

(Haskell)
a145654 n = a145654_list !! (n-1)
a145654_list = scanl1 (+) $ tail a000918_list
-- Reinhard Zumkeller, Nov 06 2013

Crossrefs

Cf. A000217, A000295, A000918, A005803, A121173.

Sequence in context: A094939 A006732 A005803 * A221880 A295141 A074352

Adjacent sequences: A145651 A145652 A145653 * A145655 A145656 A145657

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Oct 16 2008

Extensions

Edited by R. J. Mathar, Oct 21 2008

Status

approved