OFFSET
5,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 5..1000
Index entries for linear recurrences with constant coefficients, signature (1,5,-5,-10,10,10,-10,-5,5,1,-1).
FORMULA
From Colin Barker, Nov 28 2014: (Start)
a(n) = ((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680 for n>5.
G.f.: x^5*(1 -5*x^2 +x^3 +11*x^4 -3*x^5 -12*x^6 +5*x^7 +7*x^8 -3*x^9 -2*x^10 + x^11)/((1-x)^6*(1+x)^5). (End)
MAPLE
seq( `if`(n=5, 1, ((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680), n=5..50); # G. C. Greubel, Jan 24 2020
MATHEMATICA
Table[If[n==5, 1, ((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680], {n, 5, 50}] (* G. C. Greubel, Jan 24 2020 *)
LinearRecurrence[{1, 5, -5, -10, 10, 10, -10, -5, 5, 1, -1}, {1, 1, 1, 2, 3, 5, 8, 13, 20, 32, 46, 72}, 50] (* Harvey P. Dale, Mar 08 2023 *)
PROG
(PARI) vector(50, n, my(m=n+4); if(m==5, 1, ((2*m^5 -45*m^4 +450*m^3 -2070*m^2 +4873*m -3585) +5*(-1)^m*(m^4 -34*m^3 +446*m^2 -2741*m +6861))/7680)) \\ G. C. Greubel, Jan 24 2020
(Magma) [1] cat [((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680: n in [6..50]]; // G. C. Greubel, Jan 24 2020
(Sage) [1]+[((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680 for n in (6..50)] # G. C. Greubel, Jan 24 2020
(GAP) Concatenation([1], List([6..50], n-> ((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680 )); # G. C. Greubel, Jan 24 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 28 2000
STATUS
approved