A177469 Expansion of (1-x+38*x^2-72*x^3-8*x^4+30*x^5) / (1-8*x -66*x^2 +280*x^3 +178*x^4 -532*x^5 -84*x^6 +108*x^7).

1, 7, 160, 1390, 19534, 202528, 2495596, 27700276, 326878816, 3718923448, 43234331704, 496209443344, 5738582748400, 66066860825968, 762649926287584, 8789761525471360, 101400012042254944, 1169112414739169152, 13483991218981408192, 155487427811428691968

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..940

S. Kitaev, A. Burstein and T. Mansour, Counting independent sets in certain classes of (almost) regular graphs, Pure Mathematics and Applications (PU.M.A.) 19 (2008), no. 2-3, 17-26.

Index entries for linear recurrences with constant coefficients, signature (8, 66, -280, -178, 532, 84, -108).

Formula

G.f.: (1-x+38*x^2-72*x^3-8*x^4+30*x^5) / (1-8*x -66*x^2 +280*x^3 +178*x^4 -532*x^5 -84*x^6 +108*x^7).

a(0)=1, a(1)=7, a(2)=160, a(3)=1390, a(4)=19534, a(5)=202528, a(6)=2495596, a(n)=8*a(n-1) +66*a(n-2) -280*a(n-3) -178*a(n-4) +532*a(n-5)+ 84*a(n-6)-108*a(n-7). - Harvey P. Dale, Jul 04 2011

Maple

f:= gfun:-rectoproc({a(0)=1, a(1)=7, a(2)=160, a(3)=1390, a(4)=19534, a(5)=202528, a(6)=2495596, a(n)=8*a(n-1) +66*a(n-2) -280*a(n-3) -178*a(n-4) +532*a(n-5)+ 84*a(n-6)-108*a(n-7)}, a(n), remember):
seq(f(n), n=0..30); # Robert Israel, Dec 21 2015

Mathematica

CoefficientList[Series[(1-x+38x^2-72x^3-8x^4+30x^5)/ (1-8x-66x^2+ 280x^3+ 178x^4- 532x^5- 84x^6+108x^7), {x, 0, 20}], x]  (* or *) LinearRecurrence[ {8, 66, -280, -178, 532, 84, -108}, {1, 7, 160, 1390, 19534, 202528, 2495596}, 21] (* Harvey P. Dale, Jul 04 2011 *)

Prog

(Magma) I:=[1, 7, 160, 1390, 19534, 202528, 2495596]; [n le 7 select I[n] else 8*Self(n-1)+66*Self(n-2)-280*Self(n-3)-178*Self(n-4)+532*Self(n-5)+84*Self(n-6)-108*Self(n-7): n in [1..30]]; // Vincenzo Librandi, Dec 22 2015

Crossrefs

Sequence in context: A153713 A137995 A177779 * A121786 A316947 A083153

Adjacent sequences: A177466 A177467 A177468 * A177470 A177471 A177472

Keyword

nonn

Author

Signy Olafsdottir (signy06(AT)ru.is), May 09 2010

Status

approved