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 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 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. A063196. Cf. A181900, A022998, A001082. 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

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Last modified May 28 04:36 EDT 2020. Contains 334671 sequences. (Running on oeis4.)