The OEIS is supported by the many generous donors to the OEIS 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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A274497 Sum of the degrees of asymmetry of all binary words of length n. 3
 0, 0, 2, 4, 16, 32, 96, 192, 512, 1024, 2560, 5120, 12288, 24576, 57344, 114688, 262144, 524288, 1179648, 2359296, 5242880, 10485760, 23068672, 46137344, 100663296, 201326592, 436207616, 872415232, 1879048192, 3758096384, 8053063680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The degree of asymmetry of a finite sequence of numbers is defined to be the number of pairs of symmetrically positioned distinct entries. Example: the degree of asymmetry of (2,7,6,4,5,7,3) is 2, counting the pairs (2,3) and (6,5). A sequence is palindromic if and only if its degree of asymmetry is 0. LINKS Index entries for linear recurrences with constant coefficients, signature (2,4,-8). FORMULA a(n) = (1/8)*(2n - 1 + (-1)^n)*2^n. a(n) = Sum_{k>=0} k*A274496(n,k). From Alois P. Heinz, Jul 27 2016: (Start) a(n) = 2^(n-1) * A004526(n) = 2^(n-1)*floor(n/2). a(n) = 2 * A134353(n-2) for n>=2. (End) From Chai Wah Wu, Dec 27 2018: (Start) a(n) = 2*a(n-1) + 4*a(n-2) - 8*a(n-3) for n > 2. G.f.: 2*x^2/((2*x - 1)^2*(2*x + 1)). (End) EXAMPLE a(3) = 4 because the binary words 000, 001, 010, 100, 011, 101, 110, 111 have degrees of asymmetry 0, 1, 0, 1, 1, 0, 1, 0, respectively. MAPLE a:= proc(n) options operator, arrow: (1/8)*(2*n-1+(-1)^n)*2^n end proc: seq(a(n), n = 0 .. 30); MATHEMATICA LinearRecurrence[{2, 4, -8}, {0, 0, 2}, 31] (* Jean-François Alcover, Nov 16 2022 *) CROSSREFS Cf. A004526, A134353, A274496, A274498, A274499. Sequence in context: A032464 A171381 A334083 * A145119 A081411 A269758 Adjacent sequences: A274494 A274495 A274496 * A274498 A274499 A274500 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jul 27 2016 STATUS approved

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

Last modified December 6 16:00 EST 2022. Contains 358644 sequences. (Running on oeis4.)