A203551 a(n) = n*(5n^2 + 3n + 4) / 6.

0, 2, 10, 29, 64, 120, 202, 315, 464, 654, 890, 1177, 1520, 1924, 2394, 2935, 3552, 4250, 5034, 5909, 6880, 7952, 9130, 10419, 11824, 13350, 15002, 16785, 18704, 20764, 22970, 25327, 27840, 30514, 33354, 36365, 39552, 42920, 46474, 50219

Offset: 0

Author

Michael Somos, Jan 02 2012

Keywords

• nonn
• easy

Examples

			G.f. = 2*x + 10*x^2 + 29*x^3 + 64*x^4 + 120*x^5 + 202*x^6 + 315*x^7 + 464*x^8 + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A203552.

Programs

Magma

I:=[0, 2, 10, 29]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jan 07 2012

Mathematica

LinearRecurrence[{4,-6,4,-1},{0,2,10,29},40] (* Vincenzo Librandi, Jan 07 2012 *)
Table[n (5n^2+3n+4)/6,{n,0,40}] (* Harvey P. Dale, Mar 24 2022 *)

PARI

{a(n) = n * (5*n^2 + 3*n + 4) / 6};

Formula

a(n) = Sum_{k = 1..n} A(-k, k-n-1) where A(i, j) = i^2 + i*j + j^2 + i + j + 1.

G.f.: x * (2 + 2*x + x^2) / (1 - x)^4.

a(n) = -A203552(-n) for all n in Z.

a(n)-a(n-1) = A192136(n). - Bruno Berselli, Jan 03 2012

E.g.f.: x*(5*x^2 + 18*x + 12)*exp(x)/6. - G. C. Greubel, Aug 12 2018