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A304579 a(n) = (n^2 + 1)*(n^2 + 2). 0
2, 6, 30, 110, 306, 702, 1406, 2550, 4290, 6806, 10302, 15006, 21170, 29070, 39006, 51302, 66306, 84390, 105950, 131406, 161202, 195806, 235710, 281430, 333506, 392502, 459006, 533630, 617010, 709806, 812702, 926406, 1051650, 1189190, 1339806, 1504302, 1683506 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) and A304578(n) are coprime for all n.
LINKS
Daniele Mastrostefano and Carlo Sanna, On numbers n with polynomial image coprime with the nth term of a linear recurrence, arXiv:1805.05114. [math.NT], 2018 (see 4.2, page 7).
FORMULA
G.f.: 2*(1 - 2*x + 10*x^2 + 3*x^4)/(1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = A002378(A002522(n)). - Altug Alkan, May 17 2018
Sum_{n>=0} 1/a(n) = 1/4 + coth(Pi)*Pi/2 - coth(sqrt(2)*Pi)*Pi/(2*sqrt(2)). - Amiram Eldar, Feb 24 2023
MATHEMATICA
CoefficientList[Series[2 (1 - 2 x + 10 x^2 + 3 x^4) / (1 - x)^5, {x, 0, 35}], x] (* or *) Table[(n^2 + 1) (n^2 + 2), {n, 0, 40}]
LinearRecurrence[{5, -10, 10, -5, 1}, {2, 6, 30, 110, 306}, 40] (* Harvey P. Dale, Nov 13 2022 *)
PROG
(Magma) [(n^2+1)*(n^2+2): n in [0..40]];
(PARI) a(n) = my(k=n^2+1); k*(k+1); \\ Altug Alkan, May 17 2018
CROSSREFS
Subsequence of A002378, A045619, A279019.
Sequence in context: A203461 A071758 A071760 * A036752 A065563 A035105
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 17 2018
STATUS
approved

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Last modified March 1 19:16 EST 2024. Contains 370443 sequences. (Running on oeis4.)