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
KEYWORD
nonn
AUTHOR
Jeremy Gardiner, Nov 20 2011
STATUS
approved