A185688 First differences of A060819(n-4)*A060819(n).

2, -2, 3, 5, -2, 18, -19, 43, -30, 62, -71, 111, -82, 130, -153, 209, -158, 222, -265, 337, -258, 338, -407, 495, -382, 478, -579, 683, -530, 642, -781, 901, -702, 830, -1013, 1149, -898, 1042

Offset

1,1

Comments

The sequence b(n) = A060819(n-4)*A060819(n) is -3, -1, -3, 0, 5, 3, 21, 2, 45, 15, 77, 6, 117, 35, 165 for n>=1, an extension of A061037. Its first differences b(n+1)-b(n) = a(n) define the current sequence.

First differences of the quadrisection are a(4n+4)-a(4n) = 8+30*n.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,2,2,2,2,-1,-1,-1,-1).

Formula

a(2*n+1) + a(2*n+2) = 8*n.

G.f. ( x*(2+3*x^2+8*x^3+24*x^5+24*x^7+8*x^9-4*x^6+6*x^8+3*x^10) ) / ( (x-1)^2*(1+x)^3*(x^2+1)^3 ). - R. J. Mathar, Feb 16 2011

a(n) = -a(n-1) -a(n-2) -a(n-3) +2*a(n-4) +2*a(n-5) +2*a(n-6) +2*a(n-7) -a(n-8) -a(n-9) -a(n-10) -a(n-11).

a(n)=3*a(n-4) -3*a(n-8) +a(n-12). - Paul Curtz, Feb 17 2011

a(4n) + a(4n+1) +a(4n+2) +a(4n+3) = 2*n = A005843(n). - Paul Curtz, Feb 17 2011

Maple

A060819 := proc(n) n/igcd(n, 4) ; end proc:
A185688b := proc(n) A060819(n-4)*A060819(n) ; end proc:
A185688 := proc(n) A185688b(n+1)-A185688b(n) ; end proc: # R. J. Mathar, Feb 16 2011

Mathematica

Rest[CoefficientList[Series[(x*(2 + 3*x^2 + 8*x^3 + 24*x^5 + 24*x^7 + 8*x^9 - 4*x^6 + 6*x^8 + 3*x^10))/((x - 1)^2*(1 + x)^3*(x^2 + 1)^3), {x, 0, 50}], x]] (* G. C. Greubel, Jul 10 2017 *)
LinearRecurrence[{-1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1}, {2, -2, 3, 5, -2, 18, -19, 43, -30, 62, -71}, 40] (* Harvey P. Dale, Oct 03 2023 *)

Prog

(PARI) Vec((2+3*x^2+8*x^3+24*x^5+24*x^7+8*x^9-4*x^6+6*x^8+3*x^10)/(x-1)^2/(1+x)^3/(x^2+1)^3+O(x^99)) \\ Charles R Greathouse IV, Feb 08 2012

Crossrefs

Sequence in context: A302495 A368255 A368256 * A203955 A039638 A090926

Adjacent sequences: A185685 A185686 A185687 * A185689 A185690 A185691

Keyword

sign,easy

Author

Paul Curtz, Feb 10 2011

Status

approved