A220885 a(3)=5, a(4)=8, a(5)=12; thereafter a(n) = a(n-1) + A000931(n+7).

5, 8, 12, 19, 28, 40, 56, 77, 105, 142, 191, 256, 342, 456, 607, 807, 1072, 1423, 1888, 2504, 3320, 4401, 5833, 7730, 10243, 13572, 17982, 23824, 31563, 41815, 55396, 73387, 97220, 128792, 170616, 226021, 299417, 396646, 525447, 696072, 922102, 1221528, 1618183, 2143639, 2839720, 3761831, 4983368

Offset: 3

Author

N. J. A. Sloane, Dec 29 2012, based on an email from Ludovic Mignot, Dec 27 2012

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 3..1000
• P. Caron, J.-M. Champarnaud and L. Mignot, Multi-tilde-bar expressions and their automata, Acta Informatica, September 2012, Volume 49, Issue 6, pp 413-436. DOI 10.1007/s00236-012-0167-x. See the sequence t(k).
• Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1).

Programs

Haskell

a220885 n = a220885_list !! (n-3)
a220885_list = 5 : 8 : zs where
   zs = 12 : zipWith (+) zs (drop 13 a000931_list)
-- Reinhard Zumkeller, Feb 19 2013

Mathematica

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

Formula

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().

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]

a(n) = a(n-1) + A000931(n+7) for n > 5. - Reinhard Zumkeller, Feb 19 2013

a(n) = a(n-2) + a(n-3) + 9 for n >= 8. - Greg Dresden, May 18 2020

Extensions

Simpler definition from Reinhard Zumkeller, Dec 30 2012