A255182 Third differences of eighth powers (A001016).
1, 253, 5796, 46620, 213444, 697788, 1832292, 4131036, 8329860, 15426684, 26721828, 43858332, 68862276, 104183100, 152733924, 217931868, 303738372, 414699516, 555986340, 733435164, 953587908, 1223732412, 1551942756, 1947119580, 2419030404, 2978349948
Offset: 0
Examples
Third differences: 1, 253, 5796, 46620, 213444, ... (this sequence) Second differences: 1, 254, 6050, 52670, 266114, ... (A255178) First differences: 1, 255, 6305, 58975, 325089, ... (A022524) --------------------------------------------------------------------- The seventh powers: 1, 253, 5796, 46620, 213444, ... (A001016) ---------------------------------------------------------------------
Links
- Luciano Ancora, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
-
Magma
[1,253] cat [84*(2*n-1)*(2*n^4-4*n^3+8*n^2-6*n+3): n in [2..30]]; // Vincenzo Librandi, Mar 18 2015
-
Mathematica
Join[{1, 253}, Table[84 (2 n - 1) (2 n^4 - 4 n^3 + 8 n^2 - 6 n + 3), {n, 2, 30}]]
Formula
G.f.: (1 + 247*x + 4293*x^2 + 15619*x^3 + 15619*x^4 + 4293*x^5 + 247*x^6 + x^7)/(1 - x)^6.
a(n) = 84*(2*n - 1)*(2*n^4 - 4*n^3 + 8*n^2 - 6*n + 3) for n>1, a(0)=1, a(1)=253.
Extensions
Edited by Bruno Berselli, Mar 19 2015