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A322745
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a(n) = n * (16*n^2+20*n+5)^2.
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3
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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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.
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)
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EXAMPLE
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(sqrt(2) + sqrt(1))^5 = 29*sqrt(2) + 41 = sqrt(1682) + sqrt(1681). So a(1) = 1681.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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