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A136105
Partial sums of A051941.
0
6, 27, 73, 155, 285, 476, 742, 1098, 1560, 2145, 2871, 3757, 4823, 6090, 7580, 9316, 11322, 13623, 16245, 19215, 22561, 26312, 30498, 35150, 40300, 45981, 52227, 59073, 66555, 74710, 83576, 93192, 103598, 114835, 126945, 139971, 153957
OFFSET
8,1
COMMENTS
Inverse binomial transform gives 6, 21, 25, 11, 1, 0, 0, ... (0 continued). - R. J. Mathar, May 17 2008
FORMULA
a(n) = Sum_{j=8..n} Sum_{k=8..j} ((k*(k+1)/2)-30). [corrected by Jason Yuen, Sep 26 2024]
a(n) = Sum_{j=8..n} (1/6)*(j-7)*(j^2+10*j-108).
a(n) = (n-6)(n-7)(n^2+19n-144)/24. O.g.f: x^8(6-3x-2x^2)/(1-x)^5. - R. J. Mathar, May 17 2008
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) with a(8)=6, a(9)=27, a(10)=73, a(11)=155, a(12)=285. - Harvey P. Dale, Oct 20 2013
MATHEMATICA
Accumulate[LinearRecurrence[{4, -6, 4, -1}, {6, 21, 46, 82}, 50]] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {6, 27, 73, 155, 285}, 50] (* Harvey P. Dale, Oct 20 2013 *)
CROSSREFS
Cf. A051941.
Sequence in context: A085788 A027276 A101970 * A239568 A198958 A027313
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, May 10 2008
EXTENSIONS
Corrected and extended by R. J. Mathar, May 17 2008
STATUS
approved