OFFSET
1,2
COMMENTS
Also sequence found by reading the line from 1, in the direction 1, 24, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 05 2012
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 16*n^2 - 25*n + 10. - R. J. Mathar, Sep 04 2008
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1) = 1, a(2) = 24, a(3) = 79. - Harvey P. Dale, May 26 2012
G.f.: x*(1 + 21*x + 10*x^2)/(1-x)^3. - Harvey P. Dale, May 26 2012
E.g.f.: exp(x)*(10 - 9*x + 16*x^2) - 9. - Stefano Spezia, Oct 07 2019
MAPLE
seq( ((32*n -25)^2 +15)/64, n=1..40); # G. C. Greubel, Nov 09 2019
MATHEMATICA
f[n_] := 16n^2 -25n +10; Array[f, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 02 2008 *)
LinearRecurrence[{3, -3, 1}, {1, 24, 79}, 40] (* Harvey P. Dale, May 26 2012 *)
CoefficientList[Series[(1+21*x+10*x^2)/(1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Nov 08 2014 *)
PROG
(Magma) [16*n^2-25*n+10: n in [1..40]]; // Vincenzo Librandi, Nov 08 2014
(PARI) Vec(x*(1+21*x+10*x^2)/(1-x)^3 + O(x^40)) \\ Colin Barker, Nov 08 2014
(Sage) [((32*n -25)^2 +15)/64 for n in (1..40)] # G. C. Greubel, Nov 09 2019
(GAP) List([1..40], n-> ((32*n -25)^2 +15)/64); # G. C. Greubel, Nov 09 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Sep 02 2008
STATUS
approved