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 A322745 a(n) = n * (16*n^2+20*n+5)^2. 3
 0, 1681, 23762, 131043, 465124, 1275125, 2948406, 6041287, 11309768, 19740249, 32580250, 51369131, 77968812, 114594493, 163845374, 228735375, 312723856, 419746337, 554245218, 721200499, 926160500, 1175272581, 1475313862, 1833721943, 2258625624, 2758875625, 3344075306 (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 (6,-15,20,-15,6,-1). FORMULA sqrt(a(n)+1) + sqrt(a(n)) = (sqrt(n+1) + sqrt(n))^5. sqrt(a(n)+1) - sqrt(a(n)) = (sqrt(n+1) - sqrt(n))^5. From Colin Barker, Dec 25 2018: (Start) G.f.: x*(1681 + 13676*x + 13686*x^2 + 1676*x^3 + x^4) / (1 - x)^6. a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5. (End) EXAMPLE (sqrt(2) + sqrt(1))^5 = 29*sqrt(2) + 41 = sqrt(1682) + sqrt(1681). So a(1) = 1681. PROG (PARI) {a(n) = n*(16*n^2+20*n+5)^2} (PARI) concat(0, Vec(x*(1681 + 13676*x + 13686*x^2 + 1676*x^3 + x^4) / (1 - x)^6 + O(x^30))) \\ Colin Barker, Dec 25 2018 CROSSREFS Column 5 of A322699. Sequence in context: A145292 A228183 A175897 * A189654 A163009 A069331 Adjacent sequences:  A322742 A322743 A322744 * A322746 A322747 A322748 KEYWORD nonn,easy AUTHOR Seiichi Manyama, Dec 25 2018 STATUS approved

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Last modified March 29 21:29 EDT 2020. Contains 333117 sequences. (Running on oeis4.)