A072853 Number of permutations satisfying i-2<=p(i)<=i+6, i=1..n.
1, 2, 6, 18, 54, 162, 486, 1394, 3991, 11593, 33772, 98320, 286072, 831952, 2418664, 7030816, 20441944, 59441521, 172843609, 502580846, 1461344622, 4249102850, 12354982862, 35924300898, 104456501102, 303726483778, 883140022543
Offset: 1
Keywords
Links
- R. H. Hardin, Table of n, a(n) for n=1..400
- Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-135
- Index entries for linear recurrences with constant coefficients, signature (1, 2, 4, 8, 14, 26, 44, 56, -11, -19, -28, -28, 0, -8, -20, -20, 0, 5, 11, 10, 0, 0, 2, 2, 0, 0, -1, -1).
Formula
Recurrence: a(n)= a(n - 1) + 2*a(n - 2) + 4*a(n - 3) + 8*a(n - 4) + 14*a(n - 5) + 26*a(n - 6) + 44*a(n - 7) + 56*a(n - 8) - 11*a(n - 9) - 19*a(n - 10) - 28*a(n - 11) - 28*a(n - 12) - 8*a(n - 14) - 20*a(n - 15) - 20*a(n - 16) + 5*a(n - 18) + 11*a(n - 19) + 10*a(n - 20) + 2*a(n - 23) + 2*a(n - 24) - a(n - 27) - a(n - 28).
G.f.: - (x^20 + x^18 - 2*x^16 - 2*x^14 - 6*x^12 - 2*x^11 - 4*x^10 - 4*x^9 + 12*x^8 + 2*x^7 + 8*x^6 + 6*x^5 + 4*x^4 + 2*x^3 + x^2 - 1)/(x^28 + x^27 - 2*x^24 - 2*x^23 - 10*x^20 - 11*x^19 - 5*x^18 + 20*x^16 + 20*x^15 + 8*x^14 + 28*x^12 + 28*x^11 + 19*x^10 + 11*x^9 - 56*x^8 - 44*x^7 - 26*x^6 - 14*x^5 - 8*x^4 - 4*x^3 - 2*x^2 - x + 1).