A002466 A jumping problem. (Formerly M1066 N0402)

1, 1, 2, 4, 7, 13, 17, 30, 60, 107, 197, 257, 454, 908, 1619, 2981, 3889, 6870, 13740, 24499, 45109, 58849, 103958, 207916, 370723, 682597, 890513, 1573110, 3146220, 5609843, 10329173, 13475393, 23804566, 47609132, 84889091, 156302789

Offset

1,3

References

A. P. Domoryad, Mathematical Games and Pastimes. Macmillan, NY, 1964, p. 259.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,15,0,0,0,0,2).

Formula

a(1) = a(2) = 1, a(3) = 2, a(5*k+2) = a(5*k+1) + a(5*k-1), a(5*k+3) = a(5*k+2) + a(5*k+1), a(5*k+b) = a(5*k+b-1) + a(5*k+b-2) + a(5*k+b-3) for b=-1,0,1 [From Domoryad]. - Sean A. Irvine, Apr 21 2016

From Chai Wah Wu, Dec 20 2019: (Start)

a(n) = 15*a(n-5) + 2*a(n-10) for n > 10.

G.f.: x*(-2*x^9 - 2*x^6 + 2*x^5 - 7*x^4 - 4*x^3 - 2*x^2 - x - 1)/(2*x^10 + 15*x^5 - 1). (End)

Mathematica

A002466list[nmax_]:=LinearRecurrence[{0, 0, 0, 0, 15, 0, 0, 0, 0, 2}, {1, 1, 2, 4, 7, 13, 17, 30, 60, 107}, nmax]; A002466list[50]  (* Paolo Xausa, Jun 26 2023 *)

Crossrefs

Sequence in context: A002152 A163522 A255173 * A162842 A164901 A262744

Adjacent sequences: A002463 A002464 A002465 * A002467 A002468 A002469

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Apr 21 2016

Status

approved