cp's OEIS Frontend

A247707 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape T; triangle T(n,k), n>=0, 0<=k<=max(0,floor(2*(n-1)/3)), read by rows.

%I A247707 #15 Feb 06 2017 19:04:05
%S A247707 1,1,5,50,6,437,62,2,3270,700,36,21720,5712,506,12,160593,48364,5444,
%T A247707 282,6,1209537,425638,57648,3836,122,8999307,3578302,576791,48688,
%U A247707 2226,40,66054288,29550476,5500946,558036,33400,1056,10,485082083,239927980,50762537,6035146,440480,19180,380
%N A247707 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape T; triangle T(n,k), n>=0, 0<=k<=max(0,floor(2*(n-1)/3)), read by rows.
%C A247707 Sum_{k>0} k * T(n,k) = A247740(n).
%H A247707 Alois P. Heinz, <a href="/A247707/b247707.txt">Rows n = 0..175, flattened</a>
%H A247707 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%e A247707 T(4,2) = 2:
%e A247707 ._____._.    ._._____.
%e A247707 |_. ._| |    | |_. ._|
%e A247707 | | |_. |    | ._| | |
%e A247707 | |_| | |    | | |_| |
%e A247707 | ._| |_|    |_| |_. |
%e A247707 |_|_____|    |_____|_| .
%e A247707 Triangle T(n,k) begins:
%e A247707 00 :        1;
%e A247707 01 :        1;
%e A247707 02 :        5;
%e A247707 03 :       50,        6;
%e A247707 04 :      437,       62,       2;
%e A247707 05 :     3270,      700,      36;
%e A247707 06 :    21720,     5712,     506,     12;
%e A247707 07 :   160593,    48364,    5444,    282,     6;
%e A247707 08 :  1209537,   425638,   57648,   3836,   122;
%e A247707 09 :  8999307,  3578302,  576791,  48688,  2226,   40;
%e A247707 10 : 66054288, 29550476, 5500946, 558036, 33400, 1056, 10;
%Y A247707 Row sums give A174249 or A233427(n,5).
%Y A247707 Column k=0 gives A247771.
%Y A247707 Cf. A247740.
%K A247707 nonn,tabf
%O A247707 0,3
%A A247707 _Alois P. Heinz_, Sep 22 2014