# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a030451 Showing 1-1 of 1 %I A030451 #45 Jul 02 2023 14:04:36 %S A030451 0,2,1,3,2,4,3,5,4,6,5,7,6,8,7,9,8,10,9,11,10,12,11,13,12,14,13,15,14, %T A030451 16,15,17,16,18,17,19,18,20,19,21,20,22,21,23,22,24,23,25,24,26,25,27, %U A030451 26,28,27,29,28,30,29,31,30,32,31,33,32,34,33,35,34,36,35,37,36,38,37 %N A030451 a(2*n) = n, a(2*n+1) = n+2. %C A030451 Previous name was: Once started, this mixes the natural numbers and the natural numbers shifted by 1. %C A030451 Smallest number of integer-sided squares needed to tile a 2 X n rectangle. a(5) = 4: %C A030451 ._._._._._. %C A030451 | | |_| %C A030451 |___|___|_|. - _Alois P. Heinz_, Jun 12 2013 %H A030451 Index entries for two-way infinite sequences. %H A030451 Index entries for linear recurrences with constant coefficients, signature (1, 1, -1). %F A030451 a(n) = 3/4 -(-1)^n*3/4 +n/2. %F A030451 G.f.: (2*x-x^2)/((1-x)*(1-x^2)). %F A030451 a(2n) = n, a(2n+1) = n+2. %F A030451 a(n+2) = a(n)+1. %F A030451 a(n) = -a(-3-n). %F A030451 a(n) = A110570(n,2) for n>1. - _Reinhard Zumkeller_, Jul 28 2005 %F A030451 a(n) = (n+1)-a(n-1) with n>0, a(0)=0. - _Vincenzo Librandi_, Nov 18 2010 %F A030451 a(n) = Sum_{k=1..n} (-1)^(n+k)*(k+1). - _Arkadiusz Wesolowski_, Nov 23 2012 %F A030451 a(n+1) = (a(0) + a(1) + ... + a(n))/a(n) for n>0. This formula with different initial conditions produces A008619. - _Ivan Neretin_, Apr 25 2016 %F A030451 E.g.f.: (x*exp(x) + 3*sinh(x))/2. - _Ilya Gutkovskiy_, Apr 25 2016 %F A030451 Sum_{n>=1} (-1)^n/a(n) = 1. - _Amiram Eldar_, Oct 04 2022 %p A030451 a:= n-> iquo(n, 2, 'r') +[0, 2][r+1]: %p A030451 seq(a(n), n=0..80); # _Alois P. Heinz_, Jun 12 2013 %t A030451 Riffle[# + 1, #] &@ Range[0, 37] (* or *) %t A030451 Table[3/4 - (-1)^n 3/4 + n/2, {n, 0, 72}] (* or *) %t A030451 CoefficientList[Series[(2 x - x^2)/((1 - x) (1 - x^2)), {x, 0, 72}], x] (* _Michael De Vlieger_, Apr 25 2016 *) %o A030451 (PARI) a(n)=n\2+2*(n%2) %Y A030451 Cf. A008619, A028242, A110570. %Y A030451 Row m=2 of A113881, A219158. %K A030451 nonn,easy %O A030451 0,2 %A A030451 Daniel Smith (2true(AT)gte.net) %E A030451 New name (using existing formula) from _Joerg Arndt_, Apr 26 2016 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE