OFFSET
0,2
COMMENTS
f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.
For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Jaap Spies, Dancing School Problems, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285.
Jaap Spies, Sage program for computing A079912.
Jaap Spies, Sage program for computing the polynomial a(n).
Jaap Spies, A Bit of Math, The Art of Problem Solving, Jaap Spies Publishers (2019).
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
a(0) = 1, a(1) = 8, a(2) = 133, a(3) = 1044, a(4) = 5794; for n>4, a(n) = n^7-14*n^6+126*n^5-700*n^4+2625*n^3-6342*n^2+9072*n-5840.
G.f.: -(46*x^12 -340*x^11 +931*x^10 -1808*x^9 +727*x^8 -1400*x^7 -1506*x^6 -656*x^5 -788*x^4 -148*x^3 -97*x^2 -1) / (x -1)^8. - Colin Barker, Jan 04 2015
MAPLE
seq(n^7-14*n^6+126*n^5-700*n^4+2625*n^3-6342*n^2+9072*n-5840, n=5..20);
MATHEMATICA
Join[{1, 8, 133, 1044, 5794}, Table[n^7-14n^6+126n^5-700n^4+2625n^3- 6342n^2 +9072n-5840, {n, 5, 30}]] (* Harvey P. Dale, May 03 2011 *)
PROG
(PARI) Vec(-(46*x^12 -340*x^11 +931*x^10 -1808*x^9 +727*x^8 -1400*x^7 -1506*x^6 -656*x^5 -788*x^4 -148*x^3 -97*x^2 -1) / (x -1)^8 + O(x^100)) \\ Colin Barker, Jan 04 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jaap Spies, Jan 28 2003
EXTENSIONS
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003
STATUS
approved