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

0,3

Comments

Probable answer to the riddle in A115603.

Partial sums of the squares of the terms of A116966.

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).

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

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 *)

Crossrefs

Cf A000330, A004770

Sequence in context: A115603 A074778 A162899 * A241162 A164765 A116955

Adjacent sequences: A115388 A115389 A115390 * A115392 A115393 A115394

Keyword

nonn,easy

Author

Pierre CAMI, Mar 15 2006

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

Status

approved