This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A258582 a(n) = n*(2*n + 1)*(4*n + 1)/3. 3
 0, 5, 30, 91, 204, 385, 650, 1015, 1496, 2109, 2870, 3795, 4900, 6201, 7714, 9455, 11440, 13685, 16206, 19019, 22140, 25585, 29370, 33511, 38024, 42925, 48230, 53955, 60116, 66729, 73810, 81375, 89440, 98021, 107134, 116795, 127020, 137825, 149226, 161239, 173880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First bisection of the square pyramidal numbers (A000330). LINKS Eric Weisstein's World of Mathematics, Square Pyramidal Number Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA G.f.: x*(5 + 10*x + x^2)/(1 - x)^4. a(n) = A000330(2*n). Sum_{n>0} 1/a(n) = 3*(6 - Pi - 4*log(2)) = 0.25745587... a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Vincenzo Librandi, Nov 18 2015 a(n) = A006918(4*n-1) = A053307(4*n-1) = A228706(4*n-1) for n>0. [Bruno Berselli, Nov 18 2015] a(n) = Sum_{k=1..2*n} k^2 (see the first comment).  E.g.f. exp(x)*(5*x+ 20*x^2/2+16*x^3/3!). - Wolfdieter Lang, Mar 13 2017 MAPLE A258582:=n->n*(2*n + 1)*(4*n + 1)/3: seq(A258582(n), n=0..50); # Wesley Ivan Hurt, Nov 17 2015 MATHEMATICA Table[(1/3) n (2 n + 1) (4 n + 1), {n, 0, 45}] PROG (PARI) vector(100, n, n--; n*(2*n+1)*(4*n+1)/3) \\ Altug Alkan, Nov 06 2015 (PARI) concat(0, Vec((5*x + 10*x^2 + x^3)/(1 - x)^4 + O(x^50))) \\ Altug Alkan, Nov 06 2015 (MAGMA) [n*(2*n+1)*(4*n+1)/3: n in [0..50]]; // Wesley Ivan Hurt, Nov 17 2015 CROSSREFS Cf. A000330, A001477, A005408, A016813, A053126 (partial sums), A100157. Sequence in context: A273480 A164015 A128302 * A288679 A071252 A174002 Adjacent sequences:  A258579 A258580 A258581 * A258583 A258584 A258585 KEYWORD nonn,easy AUTHOR Ilya Gutkovskiy, Nov 06 2015 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 January 17 18:48 EST 2019. Contains 319251 sequences. (Running on oeis4.)