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

1,2

Comments

Partial sums of powers of 2 repeated 3 times.

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).

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

Example

a(4) = 1+1+1+2 = 5.

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 *)

Prog

(BASIC) for i=0 to 12 : for j=1 to 3 : s=s+2^i : print s : next j : next i
(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

Crossrefs

Cf. A027383, A173862.

Sequence in context: A367630 A354531 A302835 * A341497 A332686 A069999

Adjacent sequences: A200669 A200670 A200671 * A200673 A200674 A200675

Keyword

nonn

Author

Jeremy Gardiner, Nov 20 2011

Status

approved