A163675 a(n) = n*(2*n^2 + 5*n + 19)/2.
0, 13, 37, 78, 142, 235, 363, 532, 748, 1017, 1345, 1738, 2202, 2743, 3367, 4080, 4888, 5797, 6813, 7942, 9190, 10563, 12067, 13708, 15492, 17425, 19513, 21762, 24178, 26767, 29535, 32488, 35632, 38973, 42517, 46270, 50238, 54427, 58843, 63492, 68380
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Mathematica
CoefficientList[Series[x*(13-15*x+8*x^2)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 13, 37, 78}, 50] (* Vincenzo Librandi, Mar 06 2012 *) -
PARI
x='x+O('x^50); concat([0], Vec(x*(13 -15*x +8*x^2)/(x-1)^4)) \\ G. C. Greubel, Aug 02 2017
Formula
Row sums from A163674: a(n) = Sum_{m=1..n} (2*m*n + m + n + 9).
G.f.: x*(13 - 15*x + 8*x^2)/(x-1)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
E.g.f.: (1/2)*x*(26 + 11*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 02 2017
Extensions
Edited and a(31) corrected by R. J. Mathar, Aug 05 2009