A229525 Sum of coefficients of the transform ax^2 + (4a/k - b)x + 4a/k^2 + 2b/k + c = 0 for a,b,c = 1,-1,-1, k = 1,2,3...
11, 5, 31, 11, 59, 19, 95, 29, 139, 41, 191, 55, 251, 71, 319, 89, 395, 109, 479, 131, 571, 155, 671, 181, 779, 209, 895, 239, 1019, 271, 1151, 305, 1291, 341, 1439, 379, 1595, 419, 1759, 461, 1931, 505, 2111, 551, 2299, 599, 2495, 649, 2699, 701, 2911, 755
Offset: 1
Examples
For k = 5, the coefficients are 1, 9/5, -11/25. Clearing fractions, 25, 45, -11 and 25 + 45 -11 = 59 = a[5].
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Russell Walsmith, CL-Chemy III: Hyper-Quadratics
- Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
Programs
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PARI
Vec(-x*(x^5-x^4-4*x^3-2*x^2+5*x+11)/((x-1)^3*(x+1)^3) + O(x^100)) \\ Colin Barker, Nov 02 2014
Formula
ax^2 + (4a/k - b)x + 4a/k^2 + 2b/k + c; a,b,c = 1,-1,-1, k = 1,2,3... n.
a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). G.f.: -x*(x^5-x^4-4*x^3-2*x^2+5*x+11) / ((x-1)^3*(x+1)^3). - Colin Barker, Nov 02 2014
a(n) = -(-5+3*(-1)^n)*(4+6*n+n^2)/8. - Colin Barker, Nov 03 2014
Extensions
More terms from Colin Barker, Nov 02 2014
Comments