OFFSET
1,1
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, Binary
Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
FORMULA
a(n+1) = 2*a(n) + 4^n + 1.
a(n) = 2^(2*n-1) + 2^(n-1) - 1.
a(n) = A007582(n)-1 = A056326(2n+1) = A005367(n-1)/2 = A063376(n)/2-1 = A032125(n+1)/3-1 = A056309(2n+1)/2 = A028403(n+1)/4-1 = (A001576(n)-3)/2 = (A028400(n+1)-9)/8 = Sum_{k=2..n+1} A049775(k). - Ralf Stephan, Mar 24 2004
G.f.: x*(-2+5*x) / ( (x-1)*(2*x-1)*(4*x-1) ). - R. J. Mathar, Jun 01 2011
E.g.f.: exp(x)*(exp(3*x) + exp(x) - 2)/2. - Stefano Spezia, Sep 27 2023
MATHEMATICA
LinearRecurrence[{7, -14, 8}, {2, 9, 35}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *)
Table[FromDigits[Join[PadRight[{1}, n, 0], PadRight[{}, n-2, 1]], 2], {n, 2, 30}]//Sort (* or *) Rest[CoefficientList[Series[x (-2+5x)/((x-1)(2x-1)(4x-1)), {x, 0, 30}], x]] (* Harvey P. Dale, Jul 30 2021 *)
CROSSREFS
Subsequence of A031443.
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Mar 23 2004
STATUS
approved