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A082178 Professor Umbugio's sequence A082176 divided by 2*7*53*139 = 103138. 3
0, 0, 2, 10899, 39810992, 121829149155, 337295480604452, 876041659029003999, 2177771424820078750832, 5245758933004928883671595, 12342677428608309403866939452, 28524898742328260848840112339799, 65009312944028099855926272111730472 (list; graph; refs; listen; history; text; internal format)
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*(3633*x-2) / ((1492*x-1)*(1770*x-1)*(1863*x-1)*(2141*x-1)).

(End)

MATHEMATICA

Table[(1492^n - 1770^n - 1863^n + 2141^n)/103138, {n, 0, 12}] (* Michael De Vlieger, Nov 21 2015 *)

CoefficientList[Series[-x^2 (3633*x - 2)/((1492 x - 1) (1770 x -1) (1863 x - 1) (2141 x - 1)), {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*(3633*x-2) / ((1492*x-1)*(1770*x-1)*(1863*x-1)*(2141*x-1)) + 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

CROSSREFS

Cf. A082176, A082177.

Sequence in context: A294324 A134656 A128122 * A287650 A082912 A265013

Adjacent sequences:  A082175 A082176 A082177 * A082179 A082180 A082181

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Apr 25 2003

STATUS

approved

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Last modified September 23 15:06 EDT 2020. Contains 337310 sequences. (Running on oeis4.)