A322745 a(n) = n * (16*n^2+20*n+5)^2.

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

Offset: 0

Author

Seiichi Manyama, Dec 25 2018

Keywords

• nonn
• easy

Examples

			(sqrt(2) + sqrt(1))^5 = 29*sqrt(2) + 41 = sqrt(1682) + sqrt(1681). So a(1) = 1681.
		

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).

Crossrefs

Column 5 of A322699.

Programs

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

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)