The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A297928 a(n) = 2*4^n + 3*2^n - 1. 1
 4, 13, 43, 151, 559, 2143, 8383, 33151, 131839, 525823, 2100223, 8394751, 33566719, 134242303, 536920063, 2147581951, 8590131199, 34360131583, 137439739903, 549757386751, 2199026401279, 8796099313663, 35184384671743, 140737513521151, 562950003752959, 2251799914348543 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS For n > 0, in binary, this is a 1 followed by n-1 0's followed by 10 followed by n 1's. LINKS Index entries for linear recurrences with constant coefficients, signature (7,-14,8) FORMULA G.f.: (4 - 15*x + 8*x^2)/((1 - x)*(1 - 2*x)*(1 - 4*x)). E.g.f.: 2*e^(4*x) + 3*e^(2*x) - e^x. a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3), n > 2. a(n) = A000918(n) + A085601(n). EXAMPLE a(0) = 2*4^0 + 3*2^0 - 1 = 4;   in binary, 100. a(1) = 2*4^1 + 3*2^1 - 1 = 13;  in binary, 1101. a(2) = 2*4^2 + 3*2^2 - 1 = 43;  in binary, 101011. a(3) = 2*4^3 + 3*2^3 - 1 = 151; in binary, 10010111. a(4) = 2*4^4 + 3*2^4 - 1 = 559; in binary, 1000101111. ... MATHEMATICA Table[2 4^n+3 2^n-1, {n, 0, 30}] (* or *) LinearRecurrence[{7, -14, 8}, {4, 13, 43}, 30] (* Harvey P. Dale, Apr 22 2018 *) PROG (PARI) a(n) = 2*4^n + 3*2^n - 1 (PARI) first(n) = Vec((4 - 15*x + 8*x^2)/((1 - x)*(1 - 2*x)*(1 - 4*x)) + O(x^n)) CROSSREFS A lower bound for A296807. Cf. A000918, A085601. Sequence in context: A188176 A003688 A033434 * A113986 A149426 A042767 Adjacent sequences:  A297925 A297926 A297927 * A297929 A297930 A297931 KEYWORD nonn,easy AUTHOR Iain Fox, Jan 08 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 16:49 EST 2021. Contains 349581 sequences. (Running on oeis4.)