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 A129370 a(n) = n^2 - (n-1)^2*(1 - (-1)^n)/8. 13
 0, 1, 4, 8, 16, 21, 36, 40, 64, 65, 100, 96, 144, 133, 196, 176, 256, 225, 324, 280, 400, 341, 484, 408, 576, 481, 676, 560, 784, 645, 900, 736, 1024, 833, 1156, 936, 1296, 1045, 1444, 1160, 1600, 1281, 1764, 1408 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Partial sums are A129371. LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1). FORMULA a(n) = (1/8)*( (7*n^2 + 2*n - 1) + (-1)^n*(n-1)^2 ). G.f.: x*(1 + 4*x + 5*x^2 + 4*x^3)/(1-x^2)^3. E.g.f.: (1/4)*( x*(5+4*x)*cosh(x) - (1-4*x-3*x^2)*sinh(x) ). - G. C. Greubel, Jan 31 2024 MATHEMATICA Table[n^2-(n-1)^2 (1-(-1)^n)/8, {n, 0, 50}] (* Harvey P. Dale, Oct 22 2011 *) PROG (PARI) a(n)=n^2-(n-1)^2*(1-(-1)^n)/8 \\ Charles R Greathouse IV, Sep 28 2015 (Magma) [n^2 -(n-1)^2*(n mod 2)/4: n in [0..60]]; // G. C. Greubel, Jan 31 2024 (SageMath) [n^2 -(n-1)^2*(n%2)/4 for n in range(61)] # G. C. Greubel, Jan 31 2024 CROSSREFS Cf. A000567 (odd bisection), A016742 (even bisection), A129371. Sequence in context: A312807 A312808 A249486 * A344485 A212009 A312809 Adjacent sequences: A129367 A129368 A129369 * A129371 A129372 A129373 KEYWORD easy,nonn AUTHOR Paul Barry, Apr 11 2007 STATUS approved

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Last modified July 24 07:21 EDT 2024. Contains 374575 sequences. (Running on oeis4.)