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 A100477 a(n) = 3*a(n-1) + 2*a(n-2) + a(n-3) if n>=3, otherwise a(n) = n. 3
 0, 1, 2, 8, 29, 105, 381, 1382, 5013, 18184, 65960, 239261, 867887, 3148143, 11419464, 41422565, 150254766, 545028892, 1977018773, 7171368869, 26013173045, 94359275646, 342275541897, 1241558350028, 4503585409524 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Weighted sum of the three previous terms. a(n+1) is the number of ways to tile a strip of length n with 3 colors of squares, 2 colors of dominos, and 1 color of tromino, with the restriction that if the first tile is a square, then it can only use two colors. - Greg Dresden and Bora Bursali, Aug 17 2023 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,2,1). FORMULA From R. J. Mathar, Aug 22 2008: (Start) O.g.f.: x*(1-x)/(1-3*x-2*x^2-x^3). a(n) = A108153(n) - A108153(n-1). (End) a(0)=0, a(1)=1, a(2)=2, a(n)=3*a(n-1)+2*a(n-2)+a(n-3). - Harvey P. Dale, Jun 19 2015 MATHEMATICA RecurrenceTable[{a[n]== 3a[n-1] +2a[n-2] +a[n-3], a[0]==0, a[1]==1, a[2]==2}, a, {n, 0, 26}] (* or *) CoefficientList[ Series[(x^2-x)/(x^3+2x^2+3x-1), {x, 0, 26}], x] (* Robert G. Wilson v, May 19 2015 *) LinearRecurrence[{3, 2, 1}, {0, 1, 2}, 40] (* Harvey P. Dale, Jun 19 2015 *) PROG (Perl) #!/usr/local/bin/perl -w \$d=0; \$c=1; \$b=2; print "\$d, \$c, \$b, "; \$a=0; for (;; ){ \$a=3*\$b+2*\$c+\$d; \$d=\$c; \$c=\$b; \$b=\$a; print "\$a, "; last if (\$a >2**61); } __END__ (Magma) [n le 3 select n-1 else 3*Self(n-1)+2*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, May 20 2015 (SageMath) @CachedFunction def a(n): # a = A100477 if (n<3): return n else: return 3*a(n-1)+2*a(n-2)+a(n-3) [a(n) for n in range(41)] # G. C. Greubel, Apr 06 2023 CROSSREFS Cf. A108153. Sequence in context: A365757 A208973 A365761 * A302266 A369268 A369299 Adjacent sequences: A100474 A100475 A100476 * A100478 A100479 A100480 KEYWORD nonn,easy AUTHOR gamo (gamo(AT)telecable.es), Nov 22 2004 STATUS approved

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Last modified August 13 14:10 EDT 2024. Contains 375142 sequences. (Running on oeis4.)