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A175112
First differences of A175111.
4
1, 120, 1442, 6840, 21122, 51000, 105122, 194040, 330242, 528120, 804002, 1176120, 1664642, 2291640, 3081122, 4059000, 5253122, 6693240, 8411042, 10440120, 12816002, 15576120, 18759842, 22408440, 26565122, 31275000, 36585122
OFFSET
0,2
COMMENTS
Convolution of the finite sequence 1,116,967,1672,967,116,1 with A001752. Number of points in the standard root system of the D_5 lattice having L_oo norm n.
FORMULA
a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6), n>6.
a(n) = ((2*n+1)^5-(2*n-1)^5)/2+(-1)^n, n>0.
G.f.: (116*x+967*x^2+1672*x^3+967*x^4+116*x^5+x^6+1)/((1+x)*(1-x)^5).
MATHEMATICA
CoefficientList[Series[(116*x + 967*x^2 + 1672*x^3 + 967*x^4 + 116*x^5 + x^6+1)/((1 + x)*(1 - x)^5), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)
LinearRecurrence[{4, -5, 0, 5, -4, 1}, {1, 120, 1442, 6840, 21122, 51000, 105122}, 30] (* Harvey P. Dale, Sep 12 2023 *)
PROG
(Magma) I:=[1, 120, 1442, 6840, 21122, 51000, 105122]; [n le 7 select I[n] else 4*Self(n-1) - 5*Self(n-2) + 5*Self(n-4) - 4*Self(n-5) + Self(n-6): n in [1..40]]; // Vincenzo Librandi, Dec 19 2012
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
R. J. Mathar, Feb 13 2010
STATUS
approved