A181389 Absolute difference between (sum of previous terms) and (n-th-even square) with a(1) = 2.

2, 2, 0, 12, 20, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124, 132, 140, 148, 156, 164, 172, 180, 188, 196, 204, 212, 220, 228, 236, 244, 252, 260, 268, 276, 284, 292, 300, 308, 316, 324, 332, 340, 348, 356, 364, 372, 380, 388, 396, 404, 412, 420

Offset

1,1

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

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

Formula

a(n) = 8*n - 20 for n >= 4. - Nathaniel Johnston, May 27 2011

G.f.: (-2*x*(-1 + x + x^2 - 7*x^3 + 2*x^4))/(-1 + x)^2. - Alexander R. Povolotsky, Oct 18 2010

E.g.f.: 20 + 4*exp(x)*(2*x - 5) + x*(42 + (9 - 2*x)*x)/3. - Stefano Spezia, Jan 03 2023

Sum_{n>=4} (-1)^n/a(n) = (4-Pi)/16. - Amiram Eldar, Jan 08 2023

Maple

A181389 := proc(n) local s: s:=[2, 2, 0]: if(n<=3)then return s[n]: fi: return 8*n-20: end: seq(A181389(n), n=1..100); # Nathaniel Johnston, May 27 2011

Mathematica

CoefficientList[Series[(-2*x*(-1 + x + x^2 - 7*x^3 + 2*x^4))/(-1 + x)^2, {x, 0, 50}], x] (* G. C. Greubel, Feb 22 2017 *)
LinearRecurrence[{2, -1}, {2, 2, 0, 12, 20}, 70] (* Harvey P. Dale, Feb 13 2022 *)

Prog

(PARI) my(x='x+O('x^50)); Vec((-2*x*(-1 + x + x^2 - 7*x^3 + 2*x^4))/(-1 + x)^2) \\ G. C. Greubel, Feb 22 2017

Crossrefs

Cf. A017113.

Sequence in context: A117270 A244137 A354127 * A369072 A091466 A134085

Adjacent sequences: A181386 A181387 A181388 * A181390 A181391 A181392

Keyword

easy,nonn

Author

Giovanni Teofilatto, Oct 17 2010

Status

approved