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A000463
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n followed by n^2.
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25
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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
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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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).
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FORMULA
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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
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EXAMPLE
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G.f. = x + x^2 + 2*x^3 + 4*x^4 + 3*x^5 + 9*x^6 + 4*x^7 + 16*x^8 + ...
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MAPLE
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seq(seq(n^k, k=1..2), n=1..36); # Zerinvary Lajos, Jun 29 2007
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MATHEMATICA
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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 *)
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PROG
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(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 */
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CROSSREFS
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Cf. A188652 (first differences), A188653 (second differences), A159693 (partial sums), A000290 (squares).
Sequence in context: A340896 A293779 A063379 * A358534 A137442 A350150
Adjacent sequences: A000460 A000461 A000462 * A000464 A000465 A000466
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KEYWORD
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nonn,easy,look
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AUTHOR
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Dominick Cancilla
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EXTENSIONS
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Square of 14 corrected by Sean A. Irvine, Oct 25 2010
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STATUS
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approved
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