[seqfan] Linear recurrences with coefficients 1

Ron Hardin rhhardin at att.net
Mon Oct 20 21:56:56 CEST 2014

```This just came up.  Without looking into it yet, I wonder if there's a class of combinatorial problems varied from this for various length recurrences

/tmp/ekf
T(n,k)=Number of length n+6 0..k arrays with no seven consecutive terms having four times the sum of any three elements equal to three times the sum of the remaining four

Table starts
...126....1792......14126.......66948.......240870........708106........1809164
...250....4586......49730......290032......1249890.......4264120.......12523980
...496...11874.....175616.....1257084......6487112......25682744.......86727506
...984...30876.....620648.....5448778.....33673760.....154701784......600707602
..1952...80354....2194096....23617364....174811880.....931904308.....4161333538
..3872..208876....7758744...102366154....907556600....5613806736....28830275130
..7680..541624...27446576...443680650...4711821902...33817920836...199757196902
.15234.1400008...97142002..1922960684..24462953912..203721491688..1384167006986
.30218.3618986..343823110..8334332160.127008089170.1227234165196..9592120648562
.59940.9363890.1217189036.36123881064.659412923000.7392963064454.66472910762904

Empirical for column k:
k=1: a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6)

rhhardin at mindspring.com
rhhardin at att.net (either)

```