A008580 Crystal ball sequence for planar net 3.6.3.6.

1, 5, 13, 27, 45, 67, 95, 125, 163, 201, 249, 295, 353, 407, 475, 537, 615, 685, 773, 851, 949, 1035, 1143, 1237, 1355, 1457, 1585, 1695, 1833, 1951, 2099, 2225, 2383, 2517, 2685, 2827, 3005, 3155, 3343, 3501, 3699, 3865, 4073, 4247, 4465, 4647, 4875, 5065

Offset

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for crystal ball sequences

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

Formula

G.f.: [(1+2x)(1+2x+2x^2+2x^3-x^4)]/[(1-x)^3(1+x)^2]. - Ralf Stephan, Apr 24 2004

From Colin Barker, Jan 26 2016: (Start)

a(n) = (18*n^2+2*(-1)^n*n+18*n-7*(-1)^n-1)/8 for n>0.

a(n) = (9*n^2+10*n-4)/4 for n>0 and even.

a(n) = (9*n^2+8*n+3)/4 for n odd. (End)

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). - Wesley Ivan Hurt, Apr 19 2023

Mathematica

Join[{1}, LinearRecurrence[{1, 2, -2, -1, 1}, {5, 13, 27, 45, 67}, 40]] (* Harvey P. Dale, Dec 03 2014 *)

Prog

(PARI) a(n)=abs([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, -1, -2, 2, 1]^n*[-1; 5; 13; 27; 45])[1, 1] \\ Charles R Greathouse IV, Jun 16 2015
(PARI) Vec((1+2*x)*(1+2*x+2*x^2+2*x^3-x^4)/((1-x)^3*(1+x)^2) + O(x^100)) \\ Colin Barker, Jan 26 2016

Crossrefs

Sequence in context: A182840 A301675 A147411 * A307275 A212151 A123326

Adjacent sequences: A008577 A008578 A008579 * A008581 A008582 A008583

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Status

approved