A220885 - OEIS

%I #29 May 21 2020 10:26:47

%S 5,8,12,19,28,40,56,77,105,142,191,256,342,456,607,807,1072,1423,1888,

%T 2504,3320,4401,5833,7730,10243,13572,17982,23824,31563,41815,55396,

%U 73387,97220,128792,170616,226021,299417,396646,525447,696072,922102,1221528,1618183,2143639,2839720,3761831,4983368

%N a(3)=5, a(4)=8, a(5)=12; thereafter a(n) = a(n-1) + A000931(n+7).

%H Reinhard Zumkeller, <a href="/A220885/b220885.txt">Table of n, a(n) for n = 3..1000</a>

%H P. Caron, J.-M. Champarnaud and L. Mignot, <a href="https://www.researchgate.net/publication/257380226_Multi-tilde-bar_expressions_and_their_automata">Multi-tilde-bar expressions and their automata</a>, Acta Informatica, September 2012, Volume 49, Issue 6, pp 413-436. DOI 10.1007/s00236-012-0167-x. See the sequence t(k).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1).

%F a(3)=5, a(4)=8, a(5)=12; thereafter a(n) = a(n-1) + Pad(n) + 2*Pad(n+1) + 2*Pad(n+2), where Pad() = A000931().

%F a(n) = a(n-1)+a(n-2)-a(n-4) for n>8. G.f.: x^3*(x^5+2*x^4-x^3-x^2+3*x+5) / ((x-1)*(x^3+x^2-1)). [_Colin Barker_, Jan 04 2013]

%F a(n) = a(n-1) + A000931(n+7) for n > 5. - _Reinhard Zumkeller_, Feb 19 2013

%F a(n) = a(n-2) + a(n-3) + 9 for n >= 8. - _Greg Dresden_, May 18 2020

%t Join[{5,8},LinearRecurrence[{1,1,0,-1},{12,19,28,40},50]] (* _Harvey P. Dale_, May 30 2014 *)

%o (Haskell)

%o a220885 n = a220885_list !! (n-3)

%o a220885_list = 5 : 8 : zs where

%o    zs = 12 : zipWith (+) zs (drop 13 a000931_list)

%o -- _Reinhard Zumkeller_, Feb 19 2013

%K nonn,easy

%O 3,1

%A _N. J. A. Sloane_, Dec 29 2012, based on an email from Ludovic Mignot, Dec 27 2012

%E Simpler definition from _Reinhard Zumkeller_, Dec 30 2012