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A152744
7 times pentagonal numbers: a(n) = 7*n*(3*n-1)/2.
5
0, 7, 35, 84, 154, 245, 357, 490, 644, 819, 1015, 1232, 1470, 1729, 2009, 2310, 2632, 2975, 3339, 3724, 4130, 4557, 5005, 5474, 5964, 6475, 7007, 7560, 8134, 8729, 9345, 9982, 10640, 11319, 12019, 12740, 13482, 14245, 15029, 15834, 16660, 17507, 18375, 19264
OFFSET
0,2
FORMULA
a(n) = (21*n^2 - 7*n)/2 = A000326(n)*7.
a(n) = a(n-1) + 21*n - 14 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010
G.f.: 7*x*(1+2*x)/(1-x)^3. - Colin Barker, Feb 14 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. - Harvey P. Dale, Aug 08 2013
a(n) = Sum_{i = 2..8} P(i,n), where P(i,m) = m*((i-2)*m-(i-4))/2. - Bruno Berselli, Jul 04 2018
E.g.f.: 7*x*(2+3*x)/2. - G. C. Greubel, Sep 01 2018
From Amiram Eldar, Feb 27 2022: (Start)
Sum_{n>=1} 1/a(n) = (9*log(3) - sqrt(3)*Pi)/21.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*(Pi*sqrt(3) - 6*log(2))/21. (End)
MATHEMATICA
Table[7n (3n-1)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 7, 35}, 50] (* Harvey P. Dale, Aug 08 2013 *)
PROG
(PARI) a(n)=7*n*(3*n-1)/2 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [7*n*(3*n-1)/2: n in [0..50]]; // G. C. Greubel, Sep 01 2018
CROSSREFS
Similar sequences are listed in A316466.
Sequence in context: A061825 A077536 A256391 * A169607 A130884 A037092
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Dec 12 2008
STATUS
approved