|
%I #42 Sep 08 2022 08:45:13
%S 11,36,76,131,201,286,386,501,631,776,936,1111,1301,1506,1726,1961,
%T 2211,2476,2756,3051,3361,3686,4026,4381,4751,5136,5536,5951,6381,
%U 6826,7286,7761,8251,8756,9276,9811,10361,10926,11506,12101,12711,13336,13976
%N a(n) = (15*n^2 + 5*n + 2)/2.
%C Icosahedral gnomic numbers: first differences of icosahedral numbers.
%C The sequence is related to other gnomons of polyhedra, known by other more familiar names: triangular (tetrahedral gnomic), hex (cubic gnomic), square pyramidal numbers (octahedral gnomic).
%H Vincenzo Librandi, <a href="/A093500/b093500.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: x*(11+3*x+x^2)/(1-x)^3. - _Colin Barker_, Apr 30 2012
%t Table[(15n^2+5n+2)/2,{n,50}] (* _Harvey P. Dale_, Jun 28 2014 *)
%o (Magma) [(15*n^2+5*n+2)/2: n in [1..50]]; // _Vincenzo Librandi_, Aug 16 2011
%o (PARI) a(n)=(15*n^2+5*n+2)/2 \\ _Charles R Greathouse IV_, Jun 16 2017
%Y Cf. A000217, A000330, A003215, A005901, A006564.
%K easy,nonn
%O 1,1
%A _Michael Joseph Halm_, May 13 2004
%E New definition from _Ralf Stephan_, Dec 01 2004
%E Name corrected by _Arkadiusz Wesolowski_, Aug 15 2011
|
