A269654 Number of length-n 0..6 arrays with no adjacent pair x,x+1 repeated.

7, 49, 343, 2395, 16681, 115902, 803434, 5556909, 38350583, 264117327, 1815254345, 12451509292, 85246693192, 582545874403, 3973788262533, 27059842131395, 183956317982661, 1248518868323747, 8460336000063413, 57241697970038501

Offset

1,1

Comments

Column 6 of A269656.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 49*a(n-1) -1071*a(n-2) +13804*a(n-3) -117159*a(n-4) +695709*a(n-5) -3021382*a(n-6) +10023853*a(n-7) -26667942*a(n-8) +59661994*a(n-9) -116448220*a(n-10) +203589267*a(n-11) -324797263*a(n-12) +479027591*a(n-13) -659300067*a(n-14) +852873532*a(n-15) -1042800234*a(n-16) +1210501656*a(n-17) -1338796662*a(n-18) +1414739998*a(n-19) -1431668679*a(n-20) +1390012356*a(n-21) -1296744764*a(n-22) +1163755845*a(n-23) -1005616962*a(n-24) +837248601*a(n-25) -671927508*a(n-26) +519927877*a(n-27) -387912963*a(n-28) +279014001*a(n-29) -193401978*a(n-30) +129119305*a(n-31) -82960080*a(n-32) +51242821*a(n-33) -30387210*a(n-34) +17270445*a(n-35) -9387672*a(n-36) +4867688*a(n-37) -2399859*a(n-38) +1120399*a(n-39) -492772*a(n-40) +202839*a(n-41) -77471*a(n-42) +27132*a(n-43) -8568*a(n-44) +2380*a(n-45) -560*a(n-46) +105*a(n-47) -14*a(n-48) +a(n-49)

Example

Some solutions for n=6
..5. .1. .1. .0. .3. .3. .2. .4. .4. .1. .5. .2. .0. .3. .4. .3
..4. .0. .1. .1. .5. .3. .5. .2. .2. .1. .3. .3. .1. .5. .3. .3
..2. .0. .2. .3. .1. .2. .1. .2. .2. .4. .0. .6. .6. .3. .1. .6
..5. .0. .2. .1. .5. .0. .1. .3. .1. .2. .4. .0. .3. .3. .3. .1
..3. .0. .2. .5. .4. .3. .1. .6. .2. .0. .0. .3. .0. .2. .0. .1
..5. .6. .2. .4. .0. .2. .1. .4. .4. .1. .2. .4. .4. .1. .6. .1

Crossrefs

Cf. A269656.

Sequence in context: A269688 A269492 A269774 * A250359 A045584 A228439

Adjacent sequences: A269651 A269652 A269653 * A269655 A269656 A269657

Keyword

nonn

Author

R. H. Hardin, Mar 02 2016

Status

approved