The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A016886 a(n) = (5*n + 3)^2. 2
 9, 64, 169, 324, 529, 784, 1089, 1444, 1849, 2304, 2809, 3364, 3969, 4624, 5329, 6084, 6889, 7744, 8649, 9604, 10609, 11664, 12769, 13924, 15129, 16384, 17689, 19044, 20449, 21904, 23409, 24964, 26569, 28224, 29929, 31684, 33489, 35344, 37249, 39204, 41209 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Eric Weisstein's MathWorld, Polygamma Function. Wikipedia, Polygamma Function. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA From Colin Barker, Mar 29 2017: (Start) G.f.: (9 + x)*(1 + 4*x) / (1 - x)^3. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. (End) a(n) = A000290(A016885(n)). - Michel Marcus, Mar 30 2017 Sum_{n>=0} 1/a(n) = polygamma(1, 3/5)/25. - Amiram Eldar, Oct 02 2020 EXAMPLE a(0) = (5*0 + 3)^2 = 9. MATHEMATICA (5*Range[0, 40]+3)^2 (* or *) LinearRecurrence[{3, -3, 1}, {9, 64, 169}, 40] (* Harvey P. Dale, Dec 09 2016 *) CoefficientList[Series[(9 + x) (1 + 4 x)/(1 - x)^3, {x, 0, 40}], x] (* Michael De Vlieger, Mar 29 2017 *) PROG (PARI) Vec((9 + x)*(1 + 4*x) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Mar 29 2017 (MAGMA) [(5*n + 3)^2 : n in [0..50]]; // Wesley Ivan Hurt, Dec 02 2021 CROSSREFS Cf. A000290, A016885. Sequence in context: A165447 A050792 A171671 * A099761 A018201 A181888 Adjacent sequences:  A016883 A016884 A016885 * A016887 A016888 A016889 KEYWORD nonn,easy,changed AUTHOR STATUS approved

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

Last modified December 2 18:41 EST 2021. Contains 349445 sequences. (Running on oeis4.)