OFFSET
0,2
COMMENTS
The identity (16*n+1)^2 - (16*n^2+2*n)*(4)^2 = 1 can be written as a(n+1)^2 - A158056(n)*(4)^2 = 1. - Vincenzo Librandi, Feb 09 2012
This sequence gives the 18-gonal (or octadecagonal) gnomonic numbers. Name suggested by Todd Silvestri, Nov 22 2014
All elements are odd and contains subsequence A249356. - Todd Silvestri, Nov 22 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
OEIS Wiki, Gnomonic numbers
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(n) = 16*n + 1.
a(n) = 2*a(n-1) - a(n-2), a(0) = 1, a(1) = 17.
G.f.: (1+15*x)/(1-x)^2. - Vincenzo Librandi, Nov 23 2014
E.g.f.: (1 + 18*x)*exp(x). - G. C. Greubel, Sep 18 2019
MAPLE
seq(16*n+1, n=0..60); # G. C. Greubel, Sep 18 2019
MATHEMATICA
LinearRecurrence[{2, -1}, {1, 17}, 60]
Table[16*n+1, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2010 *)
a[n_Integer/; n>=0]:=16 n+1 (* Todd Silvestri, Nov 22 2014 *)
CoefficientList[Series[(1+15x)/(1-x)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Nov 23 2014 *)
PROG
(Magma) I:=[1, 17]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n)=n<<4+1 \\ Charles R Greathouse IV, Dec 23 2011
(Sage) [16*n+1 for n in (0..60)] # G. C. Greubel, Sep 18 2019
(GAP) List([0..60], n-> 16*n+1); # G. C. Greubel, Sep 18 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 12 2009
EXTENSIONS
Name clarified and offset changed by Todd Silvestri, Nov 22 2014
Edited by Vincenzo Librandi Nov 23 2014
Edited: Offset changed to 0 according to the
Todd Silvestri proposal. Name changed. - Wolfdieter Lang, Nov 29 2014
STATUS
approved