This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000463 n followed by n^2. 24
 1, 1, 2, 4, 3, 9, 4, 16, 5, 25, 6, 36, 7, 49, 8, 64, 9, 81, 10, 100, 11, 121, 12, 144, 13, 169, 14, 196, 15, 225, 16, 256, 17, 289, 18, 324, 19, 361, 20, 400, 21, 441, 22, 484, 23, 529, 24, 576, 25, 625, 26, 676, 27, 729, 28, 784, 29, 841, 30, 900, 31, 961, 32, 1024, 33, 1089, 34, 1156, 35, 1225, 36, 1296 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Eigensequence of a triangle with nonnegative integers interlaced with zeros (1, 0, 2, 0, 3, ...) as the right and left borders, with the rest zeros. - Gary W. Adamson, Aug 01 2016 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1). FORMULA a(n) = ((((-1)^(n+1))+1)/4)(n+1) - ((((-1)^(n+1))-1)/8)n^2 - Sam Alexander G.f.: (1+x-x^2+x^3)/((1-x)^3(1+x)^3). a(n) = if(n mod 2, (n+1)/2, (n/2)^2). - Gerald Hillier, Sep 25 2008 a(n) = floor((n+1) / 2) ^ (2 - n mod 2). - Reinhard Zumkeller, Aug 15 2011 E.g.f.: (x + 2)*(sinh(x) + x*cosh(x))/4. - Ilya Gutkovskiy, Aug 02 2016 EXAMPLE G.f. = x + x^2 + 2*x^3 + 4*x^4 + 3*x^5 + 9*x^6 + 4*x^7 + 16*x^8 + ... MAPLE seq(seq(n^k, k=1..2), n=1..36); # Zerinvary Lajos, Jun 29 2007 MATHEMATICA Array[{#, #^2} &, 36, 0] // Flatten Riffle[Range[40], Range[40]^2] (* Bruno Berselli, Jul 15 2013 *) a[ n_] := If[ OddQ @ n, (n + 1) / 2, n^2 / 4]; (* Michael Somos, May 28 2014 *) PROG (MAGMA) &cat[ [ n, n^2 ]: n in [1..36] ]; // Klaus Brockhaus, Apr 20 2009 (Haskell) a000463 n = a000463_list !! (n-1) a000463_list = concatMap (\x -> [x, x^2]) [1..] -- Reinhard Zumkeller, Apr 13 2011 (PARI) {a(n) = if( n%2, (n + 1) / 2, n^2 / 4)}; /* Michael Somos, May 28 2014 */ CROSSREFS Cf. A188652 (first differences), A188653 (second differences), A159693 (partial sums), A000290 (squares). Sequence in context: A155749 A198931 A063379 * A137442 A111390 A129596 Adjacent sequences:  A000460 A000461 A000462 * A000464 A000465 A000466 KEYWORD nonn,easy,look AUTHOR EXTENSIONS Square of 14 corrected by Sean A. Irvine, Oct 25 2010 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.