OFFSET
0,2
COMMENTS
Row 7 of A201552.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 1..210 from R. H. Hardin) [It was suggested that the initial terms of this b-file were wrong, but in fact they are correct. - N. J. A. Sloane, Jan 19 2019]
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).
FORMULA
Empirical: a(n) = 1+ 7*n*(n+1)*(841*n^4+1682*n^3+1568*n^2+727*n+222)/180.
Conjectures from Colin Barker, May 23 2018: (Start)
G.f.: (393 + 5384*x + 11999*x^2 + 5370*x^3 + 407*x^4 - 6*x^5 + x^6) / (1 - x)^7. -
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
a(n) = [x^(7*n)] (Sum_{k=0..2*n} x^k)^7. - Seiichi Manyama, Dec 14 2018
Barker conjectures confirmed using technique similar to A201553.
EXAMPLE
Some solutions for n=3:
..1....3....2....2....3...-2....0...-1...-2....1....0....1...-2...-3....1...-1
..3....2...-3....0...-2...-2....1...-3....1...-2....2....2....3....1....2...-1
.-3...-3....3....2...-2....1...-1....3...-3....3....1....1....0....0...-1....3
.-3...-2....2...-3....0....1....2....2...-1....1...-2...-3...-1....3....0....3
..0....0...-1....3...-1....1....2....1....1....1....1....2...-2...-1....0....2
.-1....0...-1...-1....2....3...-1...-1....1...-1...-2...-1....2....2...-2...-3
..3....0...-2...-3....0...-2...-3...-1....3...-3....0...-2....0...-2....0...-3
MATHEMATICA
a[n_] := Coefficient[Expand[Sum[x^k, {k, 0, 2n}]^7, x], x, 7n]; Array[a, 25, 0] (* Amiram Eldar, Dec 14 2018 *)
PROG
(PARI) {a(n) = polcoeff((sum(k=0, 2*n, x^k))^7, 7*n, x)} \\ Seiichi Manyama, Dec 14 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 02 2011
EXTENSIONS
a(0)=1 prepended by Seiichi Manyama, Dec 14 2018
STATUS
approved