A200672 Partial sums of A173862.
1, 2, 3, 5, 7, 9, 13, 17, 21, 29, 37, 45, 61, 77, 93, 125, 157, 189, 253, 317, 381, 509, 637, 765, 1021, 1277, 1533, 2045, 2557, 3069, 4093, 5117, 6141, 8189, 10237, 12285, 16381, 20477, 24573, 32765, 40957, 49149, 65533, 81917, 98301, 131069, 163837, 196605
Offset: 1
Keywords
Examples
a(4) = 1+1+1+2 = 5.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Shatalov A. A, The Cupola Algorithm Data And The Modulation-37 The Natural Sciences Aspect And The Using For Analysis Of Ancient Layouts, European Journal Of Natural History, 2007 No. 1, p. 35.
- Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2).
Programs
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BASIC
for i=0 to 12 : for j=1 to 3 : s=s+2^i : print s : next j : next i
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Magma
I:=[1,2,3,5]; [n le 4 select I[n] else Self(n-1) + 2*Self(n-3)- 2*Self(n-4): n in [1..50]]; // Vincenzo Librandi, Nov 16 2018
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Mathematica
CoefficientList[Series[(1 + x + x^2) / ((x - 1) (2 x^3 - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Nov 16 2018 *) Accumulate[Flatten[Table[PadRight[{},3,2^n],{n,0,20}]]] (* or *) LinearRecurrence[ {1,0,2,-2},{1,2,3,5},60] (* Harvey P. Dale, Jul 12 2022 *)
Formula
G.f.: x*(1+x+x^2) / ( (x-1)*(2*x^3-1) ). - R. J. Mathar, Nov 28 2011
a(3*n) = 3*(2^n-1) = 3*A000225(n). - Philippe Deléham, Mar 13 2013
a(n) = 2*a(n-3) + 3 for n > 3. - Yuchun Ji, Nov 16 2018
Comments