A055820 a(n) = T(n,n-3), array T as in A055818.

1, 11, 24, 43, 69, 103, 146, 199, 263, 339, 428, 531, 649, 783, 934, 1103, 1291, 1499, 1728, 1979, 2253, 2551, 2874, 3223, 3599, 4003, 4436, 4899, 5393, 5919, 6478, 7071, 7699, 8363, 9064, 9803, 10581, 11399, 12258

Offset: 3

Author

Clark Kimberling, May 28 2000

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 3..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A055818.

Programs

GAP

Concatenation([1], List([4..50], n-> (n^3 +3*n^2 -10*n -6)/6)); # G. C. Greubel, Jan 22 2020

Magma

[1] cat [(n^3 +3*n^2 -10*n -6)/6: n in [4..50]]; // G. C. Greubel, Jan 22 2020

Maple

seq( `if`(n=3, 1, (n^3 +3*n^2 -10*n -6)/6), n=3..50); # G. C. Greubel, Jan 22 2020

Mathematica

Join[{1},Table[(n^3+3n^2-10n-6)/6,{n,4,50}]] (* or *) Join[{1},LinearRecurrence[ {4,-6,4,-1},{11,24,43,69},50]] (* Harvey P. Dale, Sep 18 2011 *)

PARI

vector(50, n, my(m=n+2); if(m==3, 1, (m^3 +3*m^2 -10*m -6)/6)) \\ G. C. Greubel, Jan 22 2020

Sage

[1]+[(n^3 +3*n^2 -10*n -6)/6 for n in (4..50)] # G. C. Greubel, Jan 22 2020

Formula

a(n) = (n^3 +3*n^2 -10*n -6)/6, for n>3, with a(3) = 1.

From G. C. Greubel, Jan 22 2020: (Start)

G.f.: x^3*(1 + 7*x - 14*x^2 + 9*x^3 - 2*x^4)/(1-x)^4.

E.g.f.: (6 +12*x +3*x^2 -2*x^3 - (6 + 6*x - 6*x^2 - x^3)*exp(x))/6. (End)