A183779 - OEIS

%I #12 Jan 11 2025 10:41:21

%S 64,557,6887,74148,864671,9764363,112439612,1284649009,14750484447,

%T 169027656900,1939448495087,22241611726431,255158474995768,

%U 2926771174469677,33574663298792895,385137356737681316,4418069204679674215,50680826003378390099,581378165089337632172,6669173056280115589625

%N Half the number of (n+1) X 7 binary arrays with no 2 X 2 subblock having exactly 2 ones.

%H R. H. Hardin, <a href="/A183779/b183779.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (17, 68, -2331, 2715, 127282, -407543, -3552923, 16967238, 53329851, -373159393, -374852552, 5020944360, -530953324, -44088857196, 35340877520, 260439199152, -343900816832, -1042238954144, 1873164312128, 2773317482368, -6583718366464, -4584267066368, 15516200251392, 3621536735232, -24598780526592, 1537459224576, 25766309396480, -6673413963776, -17180213116928, 6712291491840, 6848728006656, -3277395591168, -1448477720576, 776315338752, 120259084288, -68719476736).

%F Empirical: a(n)=17*a(n-1)+68*a(n-2)-2331*a(n-3)+2715*a(n-4)+127282*a(n-5)-407543*a(n-6)-3552923*a(n-7)+16967238*a(n-8)+53329851*a(n-9)-373159393*a(n-10)-374852552*a(n-11)+5020944360*a(n-12)-530953324*a(n-13)-44088857196*a(n-14)+35340877520*a(n-15)+260439199152*a(n-16)-343900816832*a(n-17)-1042238954144*a(n-18)+1873164312128*a(n-19)+2773317482368*a(n-20)-6583718366464*a(n-21)-4584267066368*a(n-22)+15516200251392*a(n-23)+3621536735232*a(n-24)-24598780526592*a(n-25)+1537459224576*a(n-26)+25766309396480*a(n-27)-6673413963776*a(n-28)-17180213116928*a(n-29)+6712291491840*a(n-30)+6848728006656*a(n-31)-3277395591168*a(n-32)-1448477720576*a(n-33)+776315338752*a(n-34)+120259084288*a(n-35)-68719476736*a(n-36).

%F The above recurrence is correct. See A183782 for bounds on the order of the recurrence. - _Andrew Howroyd_, Jan 09 2025

%e Some solutions with a(1,1)=0 for 3 X 7:

%e ..0..0..1..1..0..0..0....0..1..1..1..1..1..1....0..1..1..0..1..1..1

%e ..0..1..1..1..1..0..0....0..0..1..1..1..1..0....1..1..1..1..1..1..1

%e ..0..0..1..1..0..0..1....0..1..1..1..1..0..0....0..1..1..0..1..1..0

%Y Column k=6 of A183782.

%K nonn,easy

%O 0,1

%A _R. H. Hardin_, Jan 07 2011

%E a(0) prepended by _Andrew Howroyd_, Jan 09 2025