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A016898 a(n) = (5*n + 4)^2. 2
16, 81, 196, 361, 576, 841, 1156, 1521, 1936, 2401, 2916, 3481, 4096, 4761, 5476, 6241, 7056, 7921, 8836, 9801, 10816, 11881, 12996, 14161, 15376, 16641, 17956, 19321, 20736, 22201, 23716, 25281, 26896, 28561, 30276, 32041, 33856, 35721, 37636, 39601, 41616 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
If Y is a fixed 2-subset of a (5n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting Y. - Milan Janjic, Oct 21 2007
Interleaving of A017318 and A017378. - Michel Marcus, Aug 26 2015
LINKS
Eric Weisstein's MathWorld, Polygamma Function.
Wikipedia, Polygamma Function.
FORMULA
From Colin Barker, Mar 30 2017: (Start)
G.f.: (16 + 33*x + x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
(End)
Sum_{n>=0} 1/a(n) = polygamma(1, 4/5)/25. - Amiram Eldar, Oct 02 2020
EXAMPLE
a(0) = (5*0 + 4)^2 = 16.
MATHEMATICA
Table[(5*n + 4)^2, {n, 0, 25}] (* Amiram Eldar, Oct 02 2020 *)
LinearRecurrence[{3, -3, 1}, {16, 81, 196}, 50] (* Harvey P. Dale, Jul 30 2023 *)
PROG
(Magma) [(5*n+4)^2: n in [0..70]]; // Vincenzo Librandi, May 02 2011
(PARI) Vec((16 + 33*x + x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, Mar 30 2017
CROSSREFS
Sequence in context: A223951 A041490 A096020 * A224135 A265154 A268198
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified June 13 15:51 EDT 2024. Contains 373389 sequences. (Running on oeis4.)