A010009 - OEIS

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A010009

a(0) = 1, a(n) = 19*n^2 + 2 for n>0.

1, 21, 78, 173, 306, 477, 686, 933, 1218, 1541, 1902, 2301, 2738, 3213, 3726, 4277, 4866, 5493, 6158, 6861, 7602, 8381, 9198, 10053, 10946, 11877, 12846, 13853, 14898, 15981, 17102, 18261, 19458, 20693, 21966, 23277, 24626, 26013, 27438, 28901, 30402, 31941

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OFFSET

0,2

COMMENTS

Apart from the first term, numbers of the form (r^2+2*s^2)*n^2+2 = (r*n)^2+(s*n-1)^2+(s*n+1)^2: in this case is r=1, s=3. After 1, all terms are in A000408. - Bruno Berselli, Feb 06 2012

LINKS

Bruno Berselli, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: (1+x)*(1+17*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012

E.g.f.: (x*(x+1)*19+2)*e^x-1. - Gopinath A. R., Feb 14 2012

Sum_{n>=0} 1/a(n) = 3/4 + sqrt(38)/76*Pi*coth(Pi*sqrt(38)/19) = 1.08111673149128.. - R. J. Mathar, May 07 2024

a(n) = A069132(n)+A069132(n+1). - R. J. Mathar, May 07 2024

MATHEMATICA

Join[{1}, 19 Range[41]^2 + 2] (* Harvey P. Dale, Feb 07 2011 *)

Join[{1}, LinearRecurrence[{3, -3, 1}, {21, 78, 173}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

PROG