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A177423 a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 10; a(0)=753, a(1)=5043, a(2)=25779, a(3)=213003, a(4)=1687623, a(5)=18171219, a(6)=73344977, a(7)=769993485, a(8)=4480470831, a(9)=17582325855, a(10)=69524390079.

%I A177423 #9 Jul 03 2023 11:35:58
%S A177423 753,5043,25779,213003,1687623,18171219,73344977,769993485,4480470831,
%T A177423 17582325855,69524390079,276487733631,1102731281151,4404485817855,
%U A177423 17605064657919,70394501404671,281526491164671,1126002935750655
%N A177423 a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 10; a(0)=753, a(1)=5043, a(2)=25779, a(3)=213003, a(4)=1687623, a(5)=18171219, a(6)=73344977, a(7)=769993485, a(8)=4480470831, a(9)=17582325855, a(10)=69524390079.
%C A177423 Related to Reverse and Add trajectory of 442 in base 2: a(n) = A075268(4*n+3)/3, i.e. one third of fourth quadrisection of A075268.
%H A177423 Vincenzo Librandi, <a href="/A177423/b177423.txt">Table of n, a(n) for n = 0..1000</a>
%H A177423 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7, -14, 8).
%F A177423 a(n) = 4^(n+8)+12576771*2^(n-4)-1 for n > 8.
%F A177423 G.f.: (753-228*x+1020*x^2+97128*x^3+517164*x^4+9133668*x^5-31930858*x^6 +497474728*x^7-28023638*x^8-3587820988*x^9+3014752848*x^10+125798400*x^11) / ((1-x)*(1-2*x)*(1-4*x)).
%F A177423 G.f. for the sequence starting at a(9): 3*x^9*(5860775285-17850630302*x +11989855016*x^2)/((1-x)*(1-2*x)*(1-4*x)).
%t A177423 CoefficientList[Series[(753 - 228 x + 1020 x^2 + 97128 x^3 + 517164 x^4 + 9133668 x^5 - 31930858 x^6 + 497474728 x^7 - 28023638 x^8 - 3587820988 x^9 + 3014752848 x^10 + 125798400 x^11)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 24 2013 *)
%o A177423 (PARI) {m=18; v=concat([753, 5043, 25779, 213003, 1687623, 18171219, 73344977, 769993485, 4480470831, 17582325855, 69524390079], vector(m-11)); for(n=12, m, v[n]=6*v[n-1]-8*v[n-2]-3); v}
%o A177423 (Magma) [753, 5043, 25779, 213003, 1687623, 18171219, 73344977, 769993485, 4480470831] cat [4^(n+8)+12576771*2^(n-4)-1: n in [9..25]]; // _Vincenzo Librandi_, Sep 24 2013
%Y A177423 Cf. A075268 (Reverse and Add trajectory of 442 in base 2), A177420, A177421, A177422.
%K A177423 nonn,easy
%O A177423 0,1
%A A177423 _Klaus Brockhaus_, May 07 2010