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A210695 a(n) = 6*a(n-1) - a(n-2) + 6 with n>1, a(0)=0, a(1)=1.

%I A210695 #50 Mar 28 2024 09:01:33
%S A210695 0,1,12,77,456,2665,15540,90581,527952,3077137,17934876,104532125,
%T A210695 609257880,3551015161,20696833092,120629983397,703083067296,
%U A210695 4097868420385,23884127455020,139206896309741,811357250403432,4728936606110857,27562262386261716
%N A210695 a(n) = 6*a(n-1) - a(n-2) + 6 with n>1, a(0)=0, a(1)=1.
%C A210695 It appears that if p is a prime of the form 8*r +/- 1, a(p-1) == 0 (mod p); and that if p is a prime of the form 8*r +/- 3, a(p+1) == 0 (mod p).
%H A210695 Bruno Berselli, <a href="/A210695/b210695.txt">Table of n, a(n) for n = 0..500</a>
%H A210695 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1).
%F A210695 G.f.: x*(1+5*x)/((1-x)*(1-6*x+x^2)). [_Bruno Berselli_, Jun 26 2012]
%F A210695 a(n) = ((1-2*sqrt(2))*(1-sqrt(2))^(2n-1)+(1+2*sqrt(2))*(1+sqrt(2))^(2n-1)-6)/4. [_Bruno Berselli_, Jun 26 2012]
%F A210695 2*a(n) = 3*A001109(n+1)-13*A001109(n)-3. - _R. J. Mathar_, Jul 18 2012
%t A210695 m = 36;n = 5; c = 0;
%t A210695 list3 = Reap[While[c < 22, t = 6 n - m + 6; Sow[t];m = n; n = t;c++]][[2,1]]
%o A210695 (Magma) [n le 2 select n-1 else 6*Self(n-1)-Self(n-2)+6: n in [1..23]]; // _Bruno Berselli_, Jun 26 2012
%Y A210695 Cf. A054490 (first differences).
%K A210695 nonn,easy
%O A210695 0,3
%A A210695 _Kenneth J Ramsey_, May 09 2012
%E A210695 Definition rewritten from _Bruno Berselli_, Jun 26 2012