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 A322677 a(n) = 16 * n * (n+1) * (2*n+1)^2. 3
 0, 288, 2400, 9408, 25920, 58080, 113568, 201600, 332928, 519840, 776160, 1117248, 1560000, 2122848, 2825760, 3690240, 4739328, 5997600, 7491168, 9247680, 11296320, 13667808, 16394400, 19509888, 23049600, 27050400, 31550688, 36590400, 42211008, 48455520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA sqrt(a(n)+1) + sqrt(a(n)) = (sqrt(n+1) + sqrt(n))^4. sqrt(a(n)+1) - sqrt(a(n)) = (sqrt(n+1) - sqrt(n))^4. a(n) = A033996(A033996(n)). Sum_{n>=1} 1/a(n) = (5 - Pi^2/2)/16 = 0.004074862465957543161422156253870277... - Vaclav Kotesovec, Dec 23 2018 From Colin Barker, Dec 23 2018: (Start) G.f.: 96*x*(3 + x)*(1 + 3*x) / (1 - x)^5. a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4. (End) EXAMPLE (sqrt(2) - sqrt(1))^4 = (sqrt(9) - sqrt(8))^2 = sqrt(289) - sqrt(288). So a(1) = 288. PROG (PARI) {a(n) = 16*n*(n+1)*(2*n+1)^2} (PARI) concat(0, Vec(96*x*(3 + x)*(1 + 3*x) / (1 - x)^5 + O(x^40))) \\ Colin Barker, Dec 23 2018 CROSSREFS sqrt(a(n)+1) + sqrt(a(n)) = (sqrt(n+1) + sqrt(n))^k: A033996(n) (k=2), A322675 (k=3), this sequence (k=4). Sequence in context: A235072 A235769 A049230 * A235552 A033692 A182026 Adjacent sequences:  A322674 A322675 A322676 * A322678 A322679 A322680 KEYWORD nonn,easy AUTHOR Seiichi Manyama, Dec 23 2018 STATUS approved

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Last modified April 4 05:34 EDT 2020. Contains 333212 sequences. (Running on oeis4.)