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A000463 n followed by n^2.

%I A000463 #55 Sep 08 2022 08:44:28
%S A000463 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,
%T A000463 169,14,196,15,225,16,256,17,289,18,324,19,361,20,400,21,441,22,484,
%U A000463 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
%N A000463 n followed by n^2.
%C A000463 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
%H A000463 Reinhard Zumkeller, <a href="/A000463/b000463.txt">Table of n, a(n) for n = 1..10000</a>
%H A000463 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A000463 a(n) = ((((-1)^(n+1))+1)/4)(n+1) - ((((-1)^(n+1))-1)/8)n^2 - _Sam Alexander_
%F A000463 G.f.: (1+x-x^2+x^3)/((1-x)^3(1+x)^3).
%F A000463 a(n) = if(n mod 2, (n+1)/2, (n/2)^2). - _Gerald Hillier_, Sep 25 2008
%F A000463 a(n) = floor((n+1) / 2) ^ (2 - n mod 2). - _Reinhard Zumkeller_, Aug 15 2011
%F A000463 E.g.f.: (x + 2)*(sinh(x) + x*cosh(x))/4. - _Ilya Gutkovskiy_, Aug 02 2016
%e A000463 G.f. = x + x^2 + 2*x^3 + 4*x^4 + 3*x^5 + 9*x^6 + 4*x^7 + 16*x^8 + ...
%p A000463 seq(seq(n^k, k=1..2), n=1..36); # _Zerinvary Lajos_, Jun 29 2007
%t A000463 Array[{#, #^2} &, 36, 0] // Flatten
%t A000463 Riffle[Range[40], Range[40]^2] (* _Bruno Berselli_, Jul 15 2013 *)
%t A000463 a[ n_] := If[ OddQ @ n, (n + 1) / 2, n^2 / 4]; (* _Michael Somos_, May 28 2014 *)
%o A000463 (Magma) &cat[ [ n, n^2 ]: n in [1..36] ]; // _Klaus Brockhaus_, Apr 20 2009
%o A000463 (Haskell)
%o A000463 a000463 n = a000463_list !! (n-1)
%o A000463 a000463_list = concatMap (\x -> [x,x^2]) [1..]
%o A000463 -- _Reinhard Zumkeller_, Apr 13 2011
%o A000463 (PARI) {a(n) = if( n%2, (n + 1) / 2, n^2 / 4)}; /* _Michael Somos_, May 28 2014 */
%Y A000463 Cf. A188652 (first differences), A188653 (second differences), A159693 (partial sums), A000290 (squares).
%K A000463 nonn,easy,look
%O A000463 1,3
%A A000463 _Dominick Cancilla_
%E A000463 Square of 14 corrected by _Sean A. Irvine_, Oct 25 2010