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

1,1

Comments

Column 1 of A251373.

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).

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

Example

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

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 *)

Crossrefs

Cf. A251373, A254598.

Sequence in context: A139184 A142235 A251373 * A152034 A348894 A142816

Adjacent sequences: A251363 A251364 A251365 * A251367 A251368 A251369

Keyword

nonn,easy

Author

R. H. Hardin, Dec 01 2014

Status

approved