OFFSET
0,3
COMMENTS
For references and details see A082176.
LINKS
Colin Barker, Table of n, a(n) for n = 0..300
H. E. G. P., Elementary problem No. E716, Professor Umbugio's Prediction, Solution by E. P. Starke, American Math. Monthly 54:1 (1947), pp. 43-44.
Index entries for linear recurrences with constant coefficients, signature (7266,-19690571,23585007306,-10533473613720).
FORMULA
From Colin Barker, Nov 21 2015: (Start)
a(n) = 7266*a(n-1) - 19690571*a(n-2) + 23585007306*a(n-3) - 10533473613720*a(n-4) for n>3.
G.f.: x^2*(2-3633*x) / ((1-1492*x)*(1-1770*x)*(1-1863*x)*(1-2141*x)). (End)
E.g.f.: exp(1492*x)*(1 - exp(278*x) - exp(371*x) + exp(649*x))/103138. - G. C. Greubel, Jan 22 2024
MATHEMATICA
Table[(1492^n - 1770^n - 1863^n + 2141^n)/103138, {n, 0, 12}] (* Michael De Vlieger, Nov 21 2015 *)
CoefficientList[Series[x^2 (2-3633*x)/((1-1492 x) (1-1770 x) (1-1863 x) (1-2141 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Nov 22 2015 *)
LinearRecurrence[{7266, -19690571, 23585007306, -10533473613720}, {0, 0, 2, 10899}, 20] (* Harvey P. Dale, Jun 25 2017 *)
PROG
(PARI) concat(vector(2), Vec(x^2*(2-3633*x) / ((1-1492*x)*(1-1770*x)*(1-1863*x)*(1-2141*x)) + O(x^15))) \\ Colin Barker, Nov 21 2015
(Magma) [(1492^n-1770^n-1863^n+2141^n)/103138 : n in [0..20]]; // Vincenzo Librandi, Nov 22 2015
(SageMath) [(1492^n-1770^n-1863^n+2141^n)/103138 for n in range(21)] # G. C. Greubel, Jan 22 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 25 2003
STATUS
approved