A082178 Professor Umbugio's sequence A082176 divided by 2*7*53*139 = 103138.

0, 0, 2, 10899, 39810992, 121829149155, 337295480604452, 876041659029003999, 2177771424820078750832, 5245758933004928883671595, 12342677428608309403866939452, 28524898742328260848840112339799, 65009312944028099855926272111730472

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)/103138 = A082176(n)/103138 = A082177(n)/53.

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

Cf. A082176, A082177.

Sequence in context: A349510 A134656 A128122 * A345396 A287650 A082912

Adjacent sequences: A082175 A082176 A082177 * A082179 A082180 A082181

Keyword

nonn,easy

Author

Wolfdieter Lang, Apr 25 2003

Status

approved