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A020974
Expansion of 1/((1-7*x)*(1-10*x)*(1-12*x)).
1
1, 29, 567, 9337, 139775, 1971417, 26715823, 352001609, 4543901439, 57765992185, 725866130639, 9039113138601, 111770394659743, 1374351994892633, 16823974751541615, 205209952708309513, 2495775222328385087, 30282093196741317561, 366714652062500686351
OFFSET
0,2
FORMULA
a(n) = 29*a(n-1) - 274*a(n-2) + 840*a(n-3) for n>=3. - Vincenzo Librandi, Mar 15 2011
a(n) = 22*a(n-1) - 120*a(n-2) + 7^n for n>1 a(0)=1, a(1)=29. - Vincenzo Librandi, Mar 15 2011
a(n) = (3*12^n+2) - 5*10^(n+2) + 2*7^(n+2))/30. - Yahia Kahloune, Jun 30 2013
MATHEMATICA
CoefficientList[Series[1/((1-7x)(1-10x)(1-12 x)), {x, 0, 50}], x] (* G. C. Greubel, May 31 2018 *)
LinearRecurrence[{29, -274, 840}, {1, 29, 567}, 30] (* Harvey P. Dale, Apr 25 2020 *)
PROG
(PARI) x='x+O('x^30); Vec(1/((1-7*x)*(1-10*x)*(1-12*x))) \\ G. C. Greubel, May 31 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-7*x)*(1-10*x)*(1-12*x)))); // G. C. Greubel, May 31 2018
CROSSREFS
Sequence in context: A025985 A020978 A023948 * A167740 A158529 A020766
KEYWORD
nonn,easy
EXTENSIONS
Terms a(16) onward added by G. C. Greubel, May 31 2018
STATUS
approved