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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
OFFSET
0,3
COMMENTS
For references and details see A082176.
LINKS
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
Sequence in context: A349510 A134656 A128122 * A345396 A287650 A082912
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 25 2003
STATUS
approved