OFFSET
4,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 4..1000
Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).
FORMULA
G.f.: x^4*(-1 +4*x^2 -x^3 -7*x^4 +2*x^5 +5*x^6 -2*x^7 -2*x^8 +x^9)/((1-x)^5 (1+x)^4). - R. J. Mathar, Jul 10 2012
From G. C. Greubel, Jan 24 2020: (Start)
a(n) = (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768 for n>4, with a(4) = 1.
E.g.f.: ( (768 -768*x +192*x^2 -64*x^3 +16*x^4) +(-768 -441*x +15*x^2 -10*x^3 +x^4)*cosh(x) +(1209 +177*x +93*x^2 -6*x^3 +x^4)*sinh(x) )/384. (End)
MAPLE
seq( `if`(n=4, 1, (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768), n=4..50); # G. C. Greubel, Jan 24 2020
MATHEMATICA
Table[If[n==4, 1, (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768], {n, 4, 50}] (* G. C. Greubel, Jan 24 2020 *)
PROG
(PARI) vector(50, n, my(m=n+3); if(m==4, 1, (2*m^4 -28*m^3 +178*m^2 -416*m +441 +(-1)^m*(4*m^3 -90*m^2 + 704*m -1977))/768)) \\ G. C. Greubel, Jan 24 2020
(Magma) [1] cat [(2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768: n in [5..50]]; // G. C. Greubel, Jan 24 2020
(Sage) [1]+[(2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768 for n in (5..50)] # G. C. Greubel, Jan 24 2020
(GAP) Concatenation([1], List([5..50], n-> (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768 )); # G. C. Greubel, Jan 24 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 28 2000
STATUS
approved