This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A222715 The number of binary pattern classes in the (2,n)-rectangular grid with 5 '1's and (2n-5) '0's: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other. 4
 2, 14, 66, 198, 508, 1092, 2156, 3876, 6606, 10626, 16478, 24570, 35672, 50344, 69624, 94248, 125562, 164502, 212762, 271502, 342804, 428076, 529828, 649740, 790790, 954954, 1145718, 1365378, 1617968, 1906128, 2234480, 2606032, 3026034, 3497886, 4027506 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 3..1000 Index entries for linear recurrences with constant coefficients, signature (3,0,-8,6,6,-8,0,3,-1). FORMULA a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6) -4*(2*n^2-22*n+63)*(-1)^n, with n>8, a(3)=2, a(4)=14, a(5)=66, a(6)=198, a(7)=508, a(8)=1092. From Bruno Berselli, May 29 2013: (Start) G.f.: 2*x^3*(1+4*x+12*x^2+8*x^3+7*x^4)/((1+x)^3*(1-x)^6). a(n) = 3*a(n-1) -8*a(n-3) +6*a(n-4) +6*a(n-5) -8*a(n-6) +3*a(n-8) -a(n-9), with n>11. a(n) = (n-2)*(n-1)*(8*n^3-16*n^2+6*n-15*(-1)^n+15)/120. (End) a(n) = (1/4)*(binomial(2*n,5) + 2*binomial(n-1,2)*(1/2)*(1-(-1)^n)). [Yosu Yurramendi and María Merino, Aug 21 2013] MATHEMATICA Table[(n - 2) (n - 1) ((8 n^3 - 16 n^2 + 6 n - 15 (-1)^n + 15)/120), {n, 3, 40}] (* Bruno Berselli, May 30 2013 *) LinearRecurrence[{3, 0, -8, 6, 6, -8, 0, 3, -1}, {2, 14, 66, 198, 508, 1092, 2156, 3876, 6606}, 50] (* T. D. Noe, Jun 14 2013 *) CoefficientList[Series[2 (1 + 4 x + 12 x^2 + 8 x^3 + 7 x^4) / ((1 + x)^3 (1 - x)^6), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 04 2013 *) PROG (MAGMA) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(2*x^3*(1+4*x+12*x^2+8*x^3+7*x^4)/((1+x)^3*(1-x)^6))); (R) a <- vector()     for(n in 1:40) a[n] <- (1/4)*(choose(2*(n+2), 5) + 2*choose(n+1, 2)*(1/2)*(1-(-1)^n))     a  [Yosu Yurramendi and María Merino, Aug 21 2013] (MAGMA) [(1/4)*(Binomial(2*n, 5) + 2*Binomial(n-1, 2)*(1/2)*(1-(-1)^n)): n in [3..40]]; // Vincenzo Librandi, Sep 04 2013 CROSSREFS Cf. A226048. Sequence in context: A266590 A196977 A254197 * A197162 A109869 A197777 Adjacent sequences:  A222712 A222713 A222714 * A222716 A222717 A222718 KEYWORD nonn,easy AUTHOR Yosu Yurramendi, May 29 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 13 12:42 EST 2019. Contains 329968 sequences. (Running on oeis4.)