A160838 G.f.: (1+38*x+263*x^2+484*x^3+263*x^4+38*x^5+x^6)/(1-x)^7.
1, 45, 557, 3473, 14417, 45965, 121997, 283137, 593281, 1147213, 2079309, 3573329, 5873297, 9295469, 14241389, 21212033, 30823041, 43821037, 61101037, 83724945, 112941137, 150205133, 197201357, 255865985, 328410881, 417348621, 525518605
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Magma
[68*n^6/45 +68*n^5/15 +91*n^4/9 +38*n^3/3 +467*n^2/45 +24*n/5 +1: n in [0..30]]; // Vincenzo Librandi, Sep 19 2011
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Mathematica
CoefficientList[Series[(1+38x+263x^2+484x^3+263x^4+38x^5+x^6)/(1-x)^7, {x,0,30}], x] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,45, 557, 3473,14417,45965,121997}, 30] (* Harvey P. Dale, Sep 17 2011 *) -
PARI
x='x+O('x^30); Vec((1+38*x+263*x^2+484*x^3+263*x^4+38*x^5+x^6)/(1-x)^7) \\ G. C. Greubel, Apr 28 2018
Formula
a(n) = 68*n^6/45 +68*n^5/15 +91*n^4/9 +38*n^3/3 +467*n^2/45 +24*n/5 +1. - R. J. Mathar, Sep 11 2011
a(0)=1, a(1)=45, a(2)=557, a(3)=3473, a(4)=14417, a(5)=45965, a(6)=121997, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)- 7*a(n-6)+a(n-7). - Harvey P. Dale, Sep 17 2011
Comments