A116413 Expansion of (1+x)/(1-2x-x^2-x^3).

1, 3, 7, 18, 46, 117, 298, 759, 1933, 4923, 12538, 31932, 81325, 207120, 527497, 1343439, 3421495, 8713926, 22192786, 56520993, 143948698, 366611175, 933692041, 2377943955, 6056191126, 15424018248, 39282171577, 100044552528, 254795294881, 648917313867

Offset

0,2

Comments

Diagonal sums of number triangle A116412. A078058 is an alternating sign version.

4*a(n) is the number of ways to tile a strip of length n+2 with red and blue squares, blue dominos, and blue trominos, where the first two tiles must have total length <= 3. - Greg Dresden and Arnim Kuchhal, Aug 05 2024

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (2,1,1).

Formula

a(n) = 2a(n-1)+a(n-2)+a(n-3).

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-k} C(k+1,j)*C(n-k-j,k)*2^(n-2k-j).

Mathematica

CoefficientList[Series[(1+x)/(1-2x-x^2-x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 1, 1}, {1, 3, 7}, 50] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2012 *)

Crossrefs

Sequence in context: A318899 A114713 A078058 * A052960 A059512 A094297

Adjacent sequences: A116410 A116411 A116412 * A116414 A116415 A116416

Keyword

easy,nonn

Author

Paul Barry, Feb 13 2006

Status

approved