A251366 Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 1 2 3 4 5 6 or 7.
79, 695, 6113, 53769, 472943, 4159927, 36590017, 321839625, 2830847119, 24899654327, 219013164449, 1926402895881, 16944315318191, 149039342816695, 1310924949760897, 11530674997804041, 101421874630758607
Offset: 1
Examples
Some solutions for n=4: 1 1 0 1 1 2 2 1 1 2 2 1 0 0 2 1 1 0 0 2 2 2 0 2 1 0 0 1 2 0 2 2 0 1 2 2 0 0 0 1 2 1 1 1 0 1 1 2 2 2 1 1 2 0 2 1 1 2 0 2 2 1 2 0 1 2 1 0 1 0 1 2 1 1 2 1 0 2 2 2 0 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
- Robert Israel, Maple-assisted proof of formula
- Index entries for linear recurrences with constant coefficients, signature (8,7).
Programs
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Maple
f:= gfun:-rectoproc({a(n) = 8*a(n-1) + 7*a(n-2), a(1)= 79, a(2)=695},a(n),remember): map(f, [$1..40]); # Robert Israel, Mar 19 2018 -
Mathematica
LinearRecurrence[{8, 7}, {79, 695}, 40] (* Jean-François Alcover, Aug 19 2022 *)
Formula
Empirical: a(n) = 8*a(n-1) + 7*a(n-2).
Empirical g.f.: x*(79 + 63*x) / (1 - 8*x - 7*x^2). - Colin Barker, Mar 19 2018
Empirical formula verified: see link.
a(n) = A254598(n+1). - Robert Israel, Mar 19 2018
Comments