A175112 First differences of A175111.

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-4,1).

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

Cf. A110907, A117216, A175114.

Sequence in context: A167549 A052776 A052770 * A257996 A183597 A027795

Adjacent sequences: A175109 A175110 A175111 * A175113 A175114 A175115

Keyword

easy,nonn

Author

R. J. Mathar, Feb 13 2010

Status

approved