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A007902 Number of pebbling configurations with n pebbles.

%I A007902 #25 Dec 24 2018 21:32:03
%S A007902 1,1,2,4,9,20,46,105,243,561,1301,3014,6995,16227,37668,87426,202961,
%T A007902 471150,1093819,2539348,5895408,13686805,31775756,73771474,171270732,
%U A007902 397628399,923150354,2143222823,4975795414,11552012449,26819637103,62265592589,144558421877
%N A007902 Number of pebbling configurations with n pebbles.
%H A007902 Alois P. Heinz, <a href="/A007902/b007902.txt">Table of n, a(n) for n = 1..1000</a>
%H A007902 F. R. K. Chung, R. L. Graham, J. A. Morrison and A. M. Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/doc/enumeration.html">Pebbling a chessboard</a>, Amer. Math. Monthly 102 (1995), pp. 113-123.
%H A007902 A. Khodulev, <a href="http://kvant.mccme.ru/1982/07/p28.htm">Pebble spreading</a>, Kvant, July 1982, pp. 28-31, 55.
%H A007902 Charles Knessl, <a href="http://dx.doi.org/10.1016/j.mcm.2007.02.010">On the number of reachable configurations for the chessboard pebbling problem</a>, Mathematical and Computer Modelling, Volume 47, Issues 1-2 (2008), 127-139.
%H A007902 M. Kontsevich, <a href="http://kvant.mccme.ru/1981/11/zadachnik_kvanta_matematika.htm">Problem M715</a>, Kvant, November 1981, p. 21.
%H A007902 Zvezdelina Stankova and Brady Haran, <a href="http://www.youtube.com/watch?v=lFQGSGsXbXE">Pebbling a Chessboard</a>, Numberphile video (2013)
%F A007902 a(n) ~ c * d^n, where d = 2.321642199494229709895447236309905876768690729938226667582430304..., c = 0.122687073421485997619475676632990508558955463577161642002764414... (Knessl, 2006). - _Vaclav Kotesovec_, Sep 06 2014
%e A007902 a(4) = 4:
%e A007902 |_|_|_|_|_   |_|_|_|_|_   |_|_|_|_|_   |_|_|_|_|_
%e A007902 |Q|_|_|_|_   |_|_|_|_|_   |_|_|_|_|_   |_|_|_|_|_
%e A007902 |_|Q|_|_|_   |Q|Q|_|_|_   |_|Q|_|_|_   |_|_|_|_|_
%e A007902 |_|Q|_|_|_   |_|_|Q|_|_   |Q|_|Q|_|_   |Q|Q|Q|_|_
%e A007902 |_|Q|_|_|_   |_|Q|_|_|_   |_|_|Q|_|_   |_|_|_|Q|_ . - _Alois P. Heinz_, Dec 20 2013
%p A007902 G:= proc(k, m) option remember; `if`(k<1, 0,
%p A007902       `if`(m=0, 2*G(k-1, 0) +G(k, 1) +`if`(k=2, 1, 0),
%p A007902       `if`(m=1, G(k-3, 0) +2*G(k-2, 1) +G(k-1, 2) +G(k-4, 1),
%p A007902        G(k-m-2, m-1) +2*G(k-m-1, m) +G(k-m, m+1))))
%p A007902     end:
%p A007902 a:= n-> `if`(n=1, 1, G(n, 0)):
%p A007902 seq(a(n), n=1..40);  # _Alois P. Heinz_, Dec 20 2013
%t A007902 G[k_, m_] := G[k, m] = If[k<1, 0, If[m == 0, 2*G[k-1, 0]+G[k, 1]+If[k == 2, 1, 0], If[m == 1, G[k-3, 0]+2*G[k-2, 1]+G[k-1, 2]+G[k-4, 1], G[k-m-2, m-1]+2*G[k-m-1, m]+G[k-m, m+1]]]]; a[n_] := If[n == 1, 1, G[n, 0]]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Feb 03 2014, after _Alois P. Heinz_ *)
%Y A007902 Cf. A007901.
%K A007902 nonn,easy,nice
%O A007902 1,3
%A A007902 odlyzko(AT)dtc.umn.edu (A. M. Odlyzko)