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 A026244 a(n) = 4^n*(4^n+1)/2. 7
 1, 10, 136, 2080, 32896, 524800, 8390656, 134225920, 2147516416, 34359869440, 549756338176, 8796095119360, 140737496743936, 2251799847239680, 36028797153181696, 576460752840294400, 9223372039002259456, 147573952598266347520, 2361183241469182345216 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 P. J. Szablowski, On moments of Cantor and related distributions, arXiv preprint arXiv:1403.0386 [math.PR], 2014. Index entries for linear recurrences with constant coefficients, signature (20,-64) FORMULA From Paul Barry, Mar 11 2004: (Start) With interpolated zeros 0, 1, 0, 10, ... has a(n) = (4^n - (-4)^n + 2*2^n - 2*(-2)^n)/16 and counts walks of length n between adjacent vertices of the 4-cube. G.f.: (1 - 10*x)/((1 - 4*x)*(1 - 16*x)). (End) From Philippe Deléham, Sep 08 2009: (Start) a(n) = Sum_{k = 0..n} 9*k*binomial(2n, 2k) = Sum_{k = 0..n} 9^k*A086645(n, k); a(n) = 8^n*T(n,5/4) where T is the Chebyshev polynomial of first kind; e.g.f.: exp(10*x)*cosh(6*x). (End) a(n) = (2*(n+1))! * [x^(2*(n+1))] (cosh(x)^4-1)/4. - Vladimir Kruchinin, Oct 19 2016 a(n) = 64^n * a(-n) for all n in Z. - Michael Somos, Jul 02 2017 MAPLE seq(binomial(-4^n, 2), n=0..18); # Zerinvary Lajos, Feb 22 2008 MATHEMATICA Table[4^n (4^n + 1)/2, {n, 0, 19}] (* Alonso del Arte, Jun 18 2019 *) PROG (MAGMA) [4^n*(4^n+1)/2: n in [0..30]]; // Vincenzo Librandi, May 01 2011 (PARI) a(n)=4^n*(4^n+1)/2 \\ Charles R Greathouse IV, Oct 07 2015 (Scala) ((List.fill(20)(4: BigInt)).scanLeft(1: BigInt)(_ * _)).map((n: BigInt) => n * (n + 1)/2) // Alonso del Arte, Jun 22 2019 CROSSREFS Cf. A052539. Sequence in context: A128862 A129803 A065024 * A261503 A096619 A276131 Adjacent sequences:  A026241 A026242 A026243 * A026245 A026246 A026247 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified June 18 12:13 EDT 2021. Contains 345098 sequences. (Running on oeis4.)