OFFSET
1,1
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..32
M. Kauers and C. Koutschan, Some D-finite and some possibly D-finite sequences in the OEIS, arXiv:2303.02793 [cs.SC], 2023.
FORMULA
From Manuel Kauers and Christoph Koutschan, Mar 01 2023: (Start)
Conjectured recurrence: a(n) - 3*a(n+1) + 2*a(n+2) - a(n+3) + 6*a(n+4) - 5*a(n+5) - 3*a(n+6) + 3*a(n+8) + 5*a(n+9) - 6*a(n+10) + a(n+11) - 2*a(n+12) + 3*a(n+13) - a(n+14) = 0.
Conjectured closed form as a quasi-polynomial:
a(6*n) = 1 + 25*n + 158*n^2 + 650*n^3 + 2275*n^4 + 4680*n^5 + 4680*n^6.
a(6*n+1) = 16 + 198*n + 1133*n^2 + 3900*n^3 + 8125*n^4 + 9360*n^5 + 4680*n^6.
a(6*n+2) = 105 + 1087*n + 4922*n^2 + 12350*n^3 + 17875*n^4 + 14040*n^5 + 4680*n^6.
a(6*n+3) = 496 + 4148*n + 14783*n^2 + 28600*n^3 + 31525*n^4 + 18720*n^5 + 4680*n^6.
a(6*n+4) = 1759 + 12121*n + 35258*n^2 + 55250*n^3 + 49075*n^4 + 23400*n^5 + 4680*n^6.
a(6*n+5) = (1+n)^2*(5052 + 19370*n + 28405*n^2 + 18720*n^3 + 4680*n^4). (End)
EXAMPLE
Some solutions for n=4:
0 0 0 0 0 0 0
0 1 2 2 1 1 1 4 4 2 4 1 0 0
2 0 2 1 0 4 0 3 0 4 2 0 2 4 2 1 0 4 3 2 3
1 0 0 0 3 3 0 0 1 3 3 1 2 0 4 3 2 4 4 4 2 3 0 2 0 2 2 0
0 0 2 1 0 0 1 1 4 0 0 1 0 1 0 0 3 2 2 0 0 4 2 2 0 0 3 1 3 0 0 0 3 0 0
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 23 2011
STATUS
approved