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A008580 Crystal ball sequence for planar net 3.6.3.6. 1
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 (list; graph; refs; listen; history; text; internal format)
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)

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

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Last modified May 17 12:55 EDT 2021. Contains 343971 sequences. (Running on oeis4.)