A115391 a(0)=0; then a(4*k+1)=a(4*k)+(4*k+1)^2, a(4*k+2)=a(4*k+1)+(4*k+3)^2, a(4*k+3)=a(4*k+2)+(4*k+2)^2, a(4*k+4)=a(4*k+3)+(4*k+4)^2.
0, 1, 10, 14, 30, 55, 104, 140, 204, 285, 406, 506, 650, 819, 1044, 1240, 1496, 1785, 2146, 2470, 2870, 3311, 3840, 4324, 4900, 5525, 6254, 6930, 7714, 8555, 9516, 10416, 11440, 12529, 13754, 14910, 16206, 17575, 19096, 20540, 22140, 23821, 25670, 27434, 29370
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000 [a(0)=0 prepended by _Georg Fischer_, Jun 18 2021]
- Index entries for linear recurrences with constant coefficients, signature (2,-1,0,2,-4,2,0,-1,2,-1).
Programs
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Mathematica
LinearRecurrence[{2,-1,0,2,-4,2,0,-1,2,-1},{0,1,10,14,30,55,104,140,204,285,406},50] (* Harvey P. Dale, Jul 01 2020 *)
Formula
G.f.: x*(4*x^7-3*x^6+8*x^5+7*x^4+12*x^3-5*x^2+8*x+1) / ((x-1)^4*(x+1)^2*(x^2+1)^2). - Colin Barker, Jul 18 2013
a(n) = (2*n+1)*(2*n*(n+1)+3*(1+cos(n*Pi)-2*cos(n*Pi/2)))/12. - Luce ETIENNE, Feb 01 2017
Extensions
More terms from Stefan Steinerberger, Mar 31 2006
Entry revised by Don Reble, Apr 06 2006
More terms from Colin Barker, Jul 18 2013
Offset adapted to definition by Georg Fischer, Jun 18 2021
Comments