The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A317613 Permutation of the nonnegative integers: lodumo_4 of A047247. 1
 2, 3, 0, 1, 4, 5, 6, 7, 10, 11, 8, 9, 12, 13, 14, 15, 18, 19, 16, 17, 20, 21, 22, 23, 26, 27, 24, 25, 28, 29, 30, 31, 34, 35, 32, 33, 36, 37, 38, 39, 42, 43, 40, 41, 44, 45, 46, 47, 50, 51, 48, 49, 52, 53, 54, 55, 58, 59, 56, 57, 60, 61, 62, 63, 66, 67, 64 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Write n in base 8, then apply the following substitution to the rightmost digit: '0'->'2, '1'->'3', and vice versa. Convert back to decimal. A self-inverse permutation: a(a(n)) = n. Array whose columns are, in this order, A047463, A047621, A047451 and A047522, read by rows. LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 OEIS wiki, Lodumo transform. Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-2,2,-1). Index entries for sequences that are permutations of the natural numbers. FORMULA a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - a(n-8), n > 7. a(n) = (4*(floor(((2*n + 4) mod 8)/4) - floor(((n + 2) mod 8)/4)) + 2*n)/2. a(n) = lod_4(A047247(n+1)). a(4*n) = A047463(n+1). a(4*n+1) = A047621(n+1). a(4*n+2) = A047451(n+1). a(4*n+3) = A047522(n+1). a(A042948(n)) = A047596(n+1). a(A042964(n+1)) = A047551(n+1). G.f.: (x^7 + x^5 + 3*x^3 - 2*x^2 - x + 2)/((x-1)^2 * (x^2+1) * (x^4+1)). E.g.f.: x*exp(x) + cos(x) + sin(x) + cos(x/sqrt(2))*cosh(x/sqrt(2)) + (sqrt(2)*cos(x/sqrt(2)) - sin(x/sqrt(2)))*sinh(x/sqrt(2)). a(n+8) = a(n) + 8 . - Philippe Deléham, Mar 09 2023 Sum_{n>=3} (-1)^(n+1)/a(n) = 1/6 + log(2). - Amiram Eldar, Mar 12 2023 EXAMPLE a(25) = a('3'1') = '3'3' = 27. a(26) = a('3'2') = '3'0' = 24. a(27) = a('3'3') = '3'1' = 25. a(28) = a('3'4') = '3'4' = 28. a(29) = a('3'5') = '3'5' = 29. The sequence as array read by rows: A047463, A047621, A047451, A047522; 2, 3, 0, 1; 4, 5, 6, 7; 10, 11, 8, 9; 12, 13, 14, 15; 18, 19, 16, 17; 20, 21, 22, 23; 26, 27, 24, 25; 28, 29, 30, 31; ... MATHEMATICA Table[(4*(Floor[1/4 Mod[2*n + 4, 8]] - Floor[1/4 Mod[n + 2, 8]]) + 2*n)/2, {n, 0, 100}] f[n_] := Block[{id = IntegerDigits[n, 8]}, FromDigits[ Join[Most@ id /. {{} -> {0}}, {id[[-1]] /. {0 -> 2, 1 -> 3, 2 -> 0, 3 -> 1}}], 8]]; Array[f, 67, 0] (* or *) CoefficientList[ Series[(x^7 + x^5 + 3x^3 - 2x^2 - x + 2)/((x - 1)^2 (x^6 + x^4 + x^2 + 1)), {x, 0, 70}], x] (* or *) LinearRecurrence[{2, -2, 2, -2, 2, -2, 2, -1}, {2, 3, 0, 1, 4, 5, 6, 7}, 70] (* Robert G. Wilson v, Aug 01 2018 *) PROG (Maxima) makelist((4*(floor(mod(2*n + 4, 8)/4) - floor(mod(n + 2, 8)/4)) + 2*n)/2, n, 0, 100); (PARI) my(x='x+O('x^100)); Vec((x^7+x^5+3*x^3-2*x^2-x+2)/((1-x)^2*(x^6+x^4+ x^2+1))) \\ G. C. Greubel, Sep 25 2018 (Magma) m:=100; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((x^7+x^5+3*x^3-2*x^2-x+2)/((1-x)^2*(x^6+x^4+ x^2+1)))); // G. C. Greubel, Sep 25 2018 CROSSREFS Cf. A047225, A047243, A047257, A064429, A080412, A159959, A026185. Sequence in context: A355889 A275736 A276074 * A292628 A163465 A360380 Adjacent sequences: A317610 A317611 A317612 * A317614 A317615 A317616 KEYWORD nonn,easy,base AUTHOR Franck Maminirina Ramaharo, Aug 01 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 00:10 EDT 2023. Contains 365532 sequences. (Running on oeis4.)