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A269640 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

%I A269640 #4 Mar 02 2016 07:47:01
%S A269640 2,3,4,4,9,6,5,16,24,9,6,25,60,63,12,7,36,120,221,159,16,8,49,210,567,
%T A269640 796,396,20,9,64,336,1209,2637,2828,969,25,10,81,504,2279,6876,12125,
%U A269640 9928,2349,30,11,100,720,3933,15307,38738,55225,34537,5640,36,12,121,990
%N A269640 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.
%C A269640 Table starts
%C A269640 ..2.....3......4.......5........6.........7.........8..........9.........10
%C A269640 ..4.....9.....16......25.......36........49........64.........81........100
%C A269640 ..6....24.....60.....120......210.......336.......504........720........990
%C A269640 ..9....63....221.....567.....1209......2279......3933.......6351.......9737
%C A269640 .12...159....796....2637.....6876.....15307.....30444......55641......95212
%C A269640 .16...396...2828...12125....38738....101999....234080.....484673.....926390
%C A269640 .20...969...9928...55225...216528....675151...1789528....4200933....8974480
%C A269640 .25..2349..34537..249600..1202353...4443665..13613507...36254755...86609789
%C A269640 .30..5640.119236.1120868..6639294..29104549.103118640..311698647..833022466
%C A269640 .36.13455.409098.5006144.36486190.189818232.778158768.2670823421.7987993868
%H A269640 R. H. Hardin, <a href="/A269640/b269640.txt">Table of n, a(n) for n = 1..9999</a>
%F A269640 Empirical for column k:
%F A269640 k=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)
%F A269640 k=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3)
%F A269640 k=3: a(n) = 9*a(n-1) -21*a(n-2) -19*a(n-3) +93*a(n-4) +27*a(n-5) -133*a(n-6) -87*a(n-7)
%F A269640 k=4: [order 7]
%F A269640 k=5: [order 13]
%F A269640 k=6: [order 14]
%F A269640 k=7: [order 16]
%F A269640 Empirical for row n:
%F A269640 n=1: a(n) = n + 1
%F A269640 n=2: a(n) = n^2 + 2*n + 1
%F A269640 n=3: a(n) = n^3 + 3*n^2 + 2*n
%F A269640 n=4: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n - 1
%F A269640 n=5: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 - 5*n + 1
%F A269640 n=6: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 - 12*n^2 + 9*n - 7 for n>2
%F A269640 n=7: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 - 22*n^3 + 28*n^2 - 37*n + 13 for n>2
%e A269640 Some solutions for n=6 k=4
%e A269640 ..4. .2. .3. .4. .3. .0. .2. .4. .0. .3. .1. .0. .4. .1. .0. .3
%e A269640 ..0. .3. .1. .2. .1. .0. .1. .3. .0. .4. .2. .2. .1. .3. .3. .2
%e A269640 ..3. .1. .2. .4. .4. .3. .4. .0. .1. .3. .0. .1. .0. .2. .0. .4
%e A269640 ..2. .4. .0. .3. .2. .1. .1. .2. .2. .0. .1. .0. .3. .0. .3. .0
%e A269640 ..1. .1. .2. .3. .2. .2. .3. .0. .4. .3. .0. .3. .2. .4. .1. .1
%e A269640 ..0. .4. .3. .0. .4. .1. .3. .2. .2. .0. .2. .0. .4. .1. .2. .1
%Y A269640 Column 1 is A002620(n+2).
%Y A269640 Column 2 is A268938.
%Y A269640 Row 1 is A000027(n+1).
%Y A269640 Row 2 is A000290(n+1).
%Y A269640 Row 3 is A007531(n+2).
%K A269640 nonn,tabl
%O A269640 1,1
%A A269640 _R. H. Hardin_, Mar 02 2016