OFFSET
0,2
LINKS
Q. H. He, J. Z. Gu, S. J. Xu, and W. H. Chan, Hosoya polynomials of hexagonal triangles and trapeziums, MATCH, Commun. Math. Comput. Chem. 72, 2014, 835-843.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = n*(66 + 407n + 670n^2 + 425n^3 + 104n^4 + 8n^5)/40 (see Corollary 3,10 in the He et al. reference).
G.f.: z*(42+150*z-39*z^2-12*z^3+3*z^4) /(1-z)^7. (Corrected by Vincenzo Librandi, Nov 15 2014)
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 > 6. - Wesley Ivan Hurt, Aug 16 2016
MAPLE
a := n -> (1/40)*n*(66 + 407*n + 670*n^2 + 425*n^3 + 104*n^4 + 8*n^5): seq(a(n), n = 0 .. 30);
MATHEMATICA
CoefficientList[Series[x (42 + 150 x - 39 x^2 - 12 x^3 + 3 x^4) / (1 - x)^7, {x, 0, 30}], x] (* Vincenzo Librandi, Nov 15 2014 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 42, 444, 2187, 7443, 20247, 47313}, 40] (* Harvey P. Dale, Oct 22 2022 *)
PROG
(Magma) [n*(66+407*n+670*n^2+425*n^3+104*n^4+8*n^5)/40: n in [0..30]]; // Vincenzo Librandi, Nov 15 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 14 2014
STATUS
approved