OFFSET
1,2
COMMENTS
Also sequence found by reading the segment (1, 20) together with the line from 20, in the direction 20, 71, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 05 2012
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Colin Barker, Aug 03 2012: (Start)
a(n) = 14 - 29*n + 16*n^2.
G.f.: x*(1 + 17*x + 14*x^2)/(1-x)^3. (End)
E.g.f.: -14 + (14 - 13*x + 16*x^2)*exp(x). - G. C. Greubel, Nov 09 2019
MAPLE
seq( ((32*n-29)^2 +55)/64, n=1..40); # G. C. Greubel, Nov 09 2019
MATHEMATICA
f[n_]:= 16n^2 -29n +14; Array[f, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 03 2008 *)
CoefficientList[Series[(1+17x+14x^2)/(1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Nov 08 2014 *)
((32*Range[50] -29)^2 +55)/64 (* G. C. Greubel, Nov 09 2019 *)
PROG
(Magma) [14-29*n+16*n^2: n in [1..50]]; // Vincenzo Librandi, Nov 08 2014
(PARI) vector(50, n, 14-29*n+16*n^2) \\ Michel Marcus, Nov 08 2014
(Sage) [((32*n-29)^2 +55)/64 for n in (1..50)] # G. C. Greubel, Nov 09 2019
(GAP) List([1..50], n-> ((32*n-29)^2 +55)/64); # G. C. Greubel, Nov 09 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Sep 03 2008
STATUS
approved