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
a(n) = (1492^n - 1770^n - 1863^n + 2141^n)/1946 = A082176(n)/1946.
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.: 53*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))/1946. - G. C. Greubel, Jan 21 2024
MAPLE
A082177:=n->(1492^n - 1770^n - 1863^n + 2141^n)/1946: seq(A082177(n), n=0..15); # Wesley Ivan Hurt, Nov 21 2015
MATHEMATICA
Table[(1492^n - 1770^n - 1863^n + 2141^n)/1946, {n, 0, 20}] (* Michael De Vlieger, Nov 21 2015 *)
CoefficientList[Series[53 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 *)
PROG
(PARI) concat(vector(2), Vec(53*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)/1946 : n in [0..15]]; // Wesley Ivan Hurt, Nov 21 2015
(Magma) I:=[0, 0, 106, 577647]; [n le 4 select I[n] else 7266*Self(n-1)-19690571*Self(n-2)+23585007306*Self(n-3)- 10533473613720*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 22 2015
(SageMath) [(1492^n - 1770^n - 1863^n + 2141^n)/1946 for n in range(21)] # G. C. Greubel, Jan 21 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 25 2003
STATUS
approved