A130862 a(n) = (n-1)*(n+2)*(2*n+11)/2.
0, 30, 85, 171, 294, 460, 675, 945, 1276, 1674, 2145, 2695, 3330, 4056, 4879, 5805, 6840, 7990, 9261, 10659, 12190, 13860, 15675, 17641, 19764, 22050, 24505, 27135, 29946, 32944, 36135, 39525, 43120, 46926, 50949, 55195, 59670, 64380, 69331, 74529, 79980, 85690, 91665, 97911, 104434, 111240, 118335, 125725, 133416, 141414
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Crossrefs
Cf. A055998.
Programs
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Magma
[(n-1)*(n+2)*(2*n+11)/2: n in [1..50]]; // Vincenzo Librandi, May 02 2011
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Mathematica
Rest[CoefficientList[Series[x^2(30-35x+11x^2)/(-1+x)^4,{x,0,30}],x]] (* or *) LinearRecurrence[{4,-6,4,-1},{0,30,85,171},30] (* Harvey P. Dale, May 01 2011 *) -
PARI
a(n)=(2*n^3 + 13*n^2 + 7*n - 22)/2 \\ Charles R Greathouse IV, May 02 2011
Formula
a(n) = (5/2)*(n+2)*(n+3)*(Sum_{j=1..n} Sum_{m=1..j} Sum_{k=1..m} (k^2-1))/(Sum_{j=1..n} Sum_{m=1..j} Sum_{k=1..m} k) = (5/2)*(n+2)*(n+3)*A130857(n)/A000332(n+3).
G.f.: x^2*(30-35*x+11*x^2)/(-1+x)^4. - R. J. Mathar, Nov 14 2007
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=0, a(1)=30, a(2)=85, a(3)=171. - Harvey P. Dale, May 01 2011
Extensions
Edited by N. J. A. Sloane, May 01 2011