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A145654
Partial sums of A000918, starting from index 1.
4
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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by R. J. Mathar, Oct 21 2008
STATUS
approved