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 A185691 Fibonacci sequence with initial terms 10 and 21. 1
 10, 21, 31, 52, 83, 135, 218, 353, 571, 924, 1495, 2419, 3914, 6333, 10247, 16580, 26827, 43407, 70234, 113641, 183875, 297516, 481391, 778907, 1260298, 2039205, 3299503, 5338708, 8638211, 13976919, 22615130, 36592049, 59207179, 95799228 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS From Wajdi Maaloul, Jun 23 2022: (Start) For n>0, a(n) is the number of ways to tile the figure below with squares and dominoes (a strip of length n+2 that contains two vertical strip of height 3 in its first and third tiles). _ _ |_| |_| |_|_|_|_____ _ |_|_|_|_|_|_|...|_| (End) LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1, 1). FORMULA From G. C. Greubel, Jul 10 2017: (Start) a(n+2) = a(n+1) + a(n) with a(0) = 10, a(1) = 21. a(n) = 11*Fibonacci(n) + 10*Fibonacci(n+1). a(n) = 9*Fibonacci(n+2) + Lucas(n+1). G.f.: (10 + 11*x)/(1 - x - x^2). E.g.f.: (1/sqrt(5))*exp(x/2)*(32*sinh(sqrt(5)*x/2) + 10*sqrt(5)*cosh(sqrt(5)*x/2)). (End) MATHEMATICA Join[{a=10, b=21}, Table[c=a+b; a=b; b=c, {n, 60}]] CoefficientList[Series[(10 + 11*x)/(1 - x - x^2), {x, 0, 50}], x] (* G. C. Greubel, Jul 10 2017 *) LinearRecurrence[{1, 1}, {10, 21}, 40] (* Harvey P. Dale, Aug 01 2024 *) PROG (PARI) x='x+O('x^50); Vec((10 + 11*x)/(1 - x - x^2)) \\ G. C. Greubel, Jul 10 2017 CROSSREFS Cf. A000032, A000045. Sequence in context: A245071 A256825 A190326 * A042291 A041194 A042871 Adjacent sequences: A185688 A185689 A185690 * A185692 A185693 A185694 KEYWORD nonn,changed AUTHOR Vladimir Joseph Stephan Orlovsky, Feb 28 2011 STATUS approved

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Last modified August 11 10:58 EDT 2024. Contains 375068 sequences. (Running on oeis4.)