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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A086500 Group the natural numbers such that the n-th group sum is divisible by the n-th triangular number: (1), (2, 3, 4), (5, 6, 7), (8, 9, 10, 11, 12), (13, 14, 15, 16, 17), (18, 19, 20, 21, 22, 23, 24), ... Sequence contains the group sum. 3
 1, 9, 18, 50, 75, 147, 196, 324, 405, 605, 726, 1014, 1183, 1575, 1800, 2312, 2601, 3249, 3610, 4410, 4851, 5819, 6348, 7500, 8125, 9477, 10206, 11774, 12615, 14415, 15376, 17424, 18513, 20825, 22050, 24642, 26011, 28899, 30420, 33620, 35301 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The number of terms in the groups is given by A063196. i.e., 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, ... Also the arithmetic mean of the n-th group is T(n), the n-th triangular number. LINKS Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1). FORMULA a(n) = n*(n+1)*(2*n+1+(-1)^n)/4. - Wesley Ivan Hurt, Sep 19 2014 a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7) for n>7. - Colin Barker, Sep 19 2014 G.f.: x*(x^4+8*x^3+6*x^2+8*x+1) / ((x-1)^4*(x+1)^3). - Colin Barker, Sep 19 2014 From Amiram Eldar, Feb 22 2022: (Start) Sum_{n>=1} 1/a(n) = 4*(1-log(2)). Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/2 - 4. (End) MATHEMATICA Table[n*(n + 1)*(2*n + 1 + (-1)^n)/4, {n, 1, 40}] (* Amiram Eldar, Feb 22 2022 *) PROG (Haskell) a086500 n = a086500_list !! (n-1) a086500_list = scanl1 (+) \$ tail a181900_list -- Reinhard Zumkeller, Mar 31 2012 (PARI) Vec(x*(x^4+8*x^3+6*x^2+8*x+1)/((x-1)^4*(x+1)^3) + O(x^100)) \\ Colin Barker, Sep 20 2014 CROSSREFS Cf. A001082, A022998, A063196, A181900. Sequence in context: A153185 A325450 A212345 * A022669 A107313 A232921 Adjacent sequences: A086497 A086498 A086499 * A086501 A086502 A086503 KEYWORD nonn,easy AUTHOR Amarnath Murthy, Jul 28 2003 EXTENSIONS More terms from Ray Chandler, Sep 17 2003 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.

Last modified March 30 18:15 EDT 2023. Contains 361622 sequences. (Running on oeis4.)