OFFSET
0,2
COMMENTS
From Bruno Berselli, Feb 06 2012: (Start)
First trisection of A005918.
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=5, s=1.
After 1, all terms are in A000408. (End)
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+25*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012
E.g.f.: (x*(x+1)*27+2)*e^x-1. - Gopinath A. R., Feb 14 2012
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3), n>=4, a(1)=29, a(2)=110, a(3)=245. - G. C. Greubel, Aug 02 2015
Sum_{n>=0} 1/a(n) = 3/4+sqrt(6)/36*Pi*coth(Pi*sqrt(6)/9) = 1.0581468172342... - R. J. Mathar, May 07 2024
MATHEMATICA
Join[{1}, 27 Range[40]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
RecurrenceTable[{a[1]==29, a[2]==110, a[3]==245, a[n]== 3*a[n-1] - 3*a[n-2] + a[n-3]}, a, {n, 1, 30}] (* G. C. Greubel, Aug 02 2015 *)
PROG
(PARI) first(m)=my(v=vector(m)); for(i=1, m, v[i]=27*(i)^2+2); concat([1], v); /* Anders Hellström, Aug 02 2015 */
(Magma) [1] cat [27*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved