login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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: A175897 A370355 A361705 * A189654 A163009 A069331
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 25 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 27 16:21 EST 2024. Contains 370378 sequences. (Running on oeis4.)