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

3,1

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).

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A314414 A314415 A314416 * A314417 A314418 A322033

Adjacent sequences: A220882 A220883 A220884 * A220886 A220887 A220888

Keyword

nonn,easy

Author

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

Extensions

Simpler definition from Reinhard Zumkeller, Dec 30 2012

Status

approved