A094311 a(n) = n*(1+n^2)*((2+n^2)^2-n^2)/16.

1, 20, 210, 1309, 5720, 19536, 55825, 139490, 314019, 650440, 1258796, 2302455, 4015570, 6724004, 10870035, 17041156, 26003285, 38738700, 56489014, 80803505, 113593116, 157190440, 214416005, 288651174, 383917975, 504966176, 657367920, 847620235, 1083255734

Offset: 1

Author

Amarnath Murthy, Apr 29 2004

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A000217, A064322.

Programs

Mathematica

Table[n(1+n^2)((2+n^2)^2-n^2)/16,{n,30}] (* or *) LinearRecurrence[ {8,-28,56,-70,56,-28,8,-1},{1,20,210,1309,5720,19536,55825,139490},30] (* Harvey P. Dale, Oct 17 2011 *)

Formula

From Harvey P. Dale, Oct 17 2011: (Start)

a(1)=1, a(2)=20, a(3)=210, a(4)=1309, a(5)=5720, a(6)=19536, a(7)=55825, a(8)=139490, a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).

G.f.: (x*(x+1)*(x*(x*(x*(x+11)+67)+66)+12)+1)/(x-1)^8. (End)

a(n) = A064322(n) - A064322(n-1). - J.S. Seneschal, Jun 27 2025

Extensions

Edited by N. J. A. Sloane following a suggestion from Zak Seidov, Mar 28 2008