A136105 Partial sums of A051941.

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

Links

Table of n, a(n) for n=8..44.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

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

Adjacent sequences: A136102 A136103 A136104 * A136106 A136107 A136108

Keyword

easy,nonn

Author

Jonathan Vos Post, May 10 2008

Extensions

Corrected and extended by R. J. Mathar, May 17 2008

Status

approved