A175717 First differences of A175628.

0, 3, 2, 3, -5, 12, 6, 3, -22, 33, 10, 3, -33, 48, 14, 3, -74, 93, 18, 3, -85, 108, 22, 3, -156, 183, 26, 3, -161, 192, 30, 3, -268, 303, 34, 3, -261, 300, 38, 3, -410, 453, 42, 3, -385, 432, 46, 3, -582, 633, 50, 3, -533, 588, 54, 3, -784, 843, 58, 3, -705, 768, 62, 3, -1016, 1083, 66, 3, -901, 972, 70

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Formula

a(2*n) + a(2*n+1) = A144396(n+1).

It seems that a(n) = 3 iff n in A131098.

a(n) = A175628(n+2) - A175628(n+1).

a(n)= -a(n-1) -a(n-2) -a(n-3) -a(n-4) -a(n-5) -a(n-6) -a(n-7) +2*a(n-8) +2*a(n-9) +2*a(n-10) +2*a(n-11) +2*a(n-12) +2*a(n-13) +2*a(n-14) +2*a(n-15) -a(n-16) -a(n-17) -a(n-18) -a(n-19) -a(n-20) -a(n-21) -a(n-22) -a(n-23). - R. J. Mathar, Dec 08 2010

From Luce ETIENNE, Dec 29 2019: (Start)

a(n) = 3*a(n-8) - 3*a(n-16) + a(n-24).

a(n) = (3*(264*m^7 - 6377*m^6 + 60963*m^5 - 293615*m^4 + 748881*m^3 - 962528*m^2 + 502812*m - 25200)*floor(n/8)^2 + 7*(136*m^7 - 3209*m^6 + 29731*m^5 - 137375*m^4 + 332209*m^3 - 400496*m^2 + 194844*m - 5040)*floor(n/8) + m*(472*m^6 - 11235*m^5 + 105049*m^4 - 488985*m^3 + 1181803*m^2 - 1389780*m + 617796))/5040, where m = n mod 8. (End)

Maple

A175628 := proc(n) if type(n, 'even') then nh := n/2 +1; 1/4-1/nh^2 ; numer(%) ; else nh := (n-1)/2 ; nh*(nh+2) ; end if; end proc:
A175717 := proc(n) A175628(n+2)-A175628(n+1) ; end proc:

Mathematica

LinearRecurrence[{-1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 3, 2, 3, -5, 12, 6, 3, -22, 33, 10, 3, -33, 48, 14, 3, -74, 93, 18, 3, -85, 108, 22}, 90] (* Harvey P. Dale, Apr 17 2015 *)
b[n_]:= If[OddQ[n], (n-1)*(n+3)/4, (n^2+4*n-12)*(37 +27*(-1)^(n/2) +6*Cos[(n+2)*Pi/4])/2^8]; Table[b[n+2] - b[n+1], {n, 0, 90}] (* G. C. Greubel, Dec 04 2019 *)

Prog

(PARI) b(n) = if(n%2==1, (n-1)*(n+3)/4, round((n^2+4*n-12)*(37 +27*(-1)^(n/2) +6*cos((n+2)*Pi/4))/2^8) );
vector(91, n, b(n+1) - b(n) ) \\ G. C. Greubel, Sep 19 2018; Dec 04 2019
(Magma) R:= RealField(20);
b:= func< n | (n mod 2) eq 1 select (n-1)*(n+3)/4 else Round((n^2+4*n-12)*(37 +27*(-1)^(n/2) +6*Cos((n+2)*Pi(R)/4))/2^8) >;
[b(n+2) b(n+1): n in [0..90]]; // G. C. Greubel, Sep 19 2018; Dec 04 2019
(Sage)
def b(n):
    if (mod(n, 2)==1): return (n-1)*(n+3)/4
    else: return round((n^2+4*n-12)*(37 +27*(-1)^(n/2) +6*cos((n+2)*pi/4))/2^8)
[b(n+2) -b(n+1) for n in (0..90)] # G. C. Greubel, Dec 04 2019

Crossrefs

Cf. A131098, A144396, A175628.

Sequence in context: A206012 A211940 A230664 * A051701 A225696 A134945

Adjacent sequences: A175714 A175715 A175716 * A175718 A175719 A175720

Keyword

sign,easy

Author

Paul Curtz, Dec 04 2010

Status

approved