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A163979 a(n) = n*(n-1) + A144437(n+2). 1
1, 3, 5, 7, 15, 23, 31, 45, 59, 73, 93, 113, 133, 159, 185, 211, 243, 275, 307, 345, 383, 421, 465, 509, 553, 603, 653, 703, 759, 815, 871, 933, 995, 1057, 1125, 1193, 1261, 1335, 1409, 1483, 1563, 1643, 1723, 1809, 1895, 1981, 2073, 2165, 2257, 2355, 2453, 2551 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First differences are 2, 2, 2, 8, 8, 8, 14, 14, 14, 20, 20, 20,... (triplicated A016933).

LINKS

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

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

FORMULA

a(n) = A002378(n-1) + A144437(n+2).

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).

G.f.: (1 +x -x^3 +5*x^4)/( (1 +x +x^2)*(1 -x)^3 ).

E.g.f.: (1/3)*((7+3*x^2)*exp(x) - 4*exp(-x/2)*cos(sqrt(3)*x/2)). - G. C. Greubel, Aug 24 2017

MATHEMATICA

LinearRecurrence[{2, -1, 1, -2, 1}, {1, 3, 5, 7, 15}, 60]  (* or *) CoefficientList[ Series[-(1+x+5x^4-x^3)/((1+x+x^2)(x-1)^3), {x, 0, 60}], x]  (* Harvey P. Dale, Apr 20 2011 *)

PROG

(PARI) x='x+O('x^50); Vec((1+x-x^3+5*x^4)/((1+x+x^2)*(1-x)^3)) \\ G. C. Greubel, Aug 24 2017

CROSSREFS

Sequence in context: A057743 A071169 A172235 * A124248 A029514 A061950

Adjacent sequences:  A163976 A163977 A163978 * A163980 A163981 A163982

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Aug 07 2009

EXTENSIONS

Edited and extended by R. J. Mathar, Aug 12 2009

STATUS

approved

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Last modified February 18 20:25 EST 2019. Contains 320262 sequences. (Running on oeis4.)