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URL: https://oeis.org/A021604

⇱ A021604 - OEIS

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A021604
Expansion of 1/((1-x)*(1-3*x)*(1-7*x)*(1-10*x)).
2
1, 21, 300, 3670, 41511, 449151, 4730890, 48987840, 501640821, 5098774681, 51564400680, 519680849610, 5225067192931, 52448485198611, 525869552045670, 5268388442396980, 52751734942121841, 527992303241992941, 5283247709746481860, 52855749840494077950, 528720407611375771551
OFFSET
0,2
FORMULA
a(n)=(8*10^(n+3) - 3*7^(n+4) + 3^(n+6) - 14)/1512. [Yahia Kahloune, Jun 26 2013]
a(0)=1, a(1)=21, a(2)=300, a(3)=3670; for n>3, a(n) = 21*a(n-1) -141*a(n-2) +331*a(n-3) -210*a(n-4). - Vincenzo Librandi, Jul 11 2013
MATHEMATICA
CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 11 2013 *)
LinearRecurrence[{21, -141, 331, -210}, {1, 21, 300, 3670}, 30] (* Harvey P. Dale, Feb 23 2014 *)
PROG
(PARI) Vec(1/((1-x)*(1-3*x)*(1-7*x)*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-7*x)*(1-10*x)))); // Vincenzo Librandi, Jul 11 2013
(Magma) I:=[1, 21, 300, 3670]; [n le 4 select I[n] else 21*Self(n-1)-141*Self(n-2)+331*Self(n-3)-210*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 11 2013
CROSSREFS
Sequence in context: A021634 A295049 A295377 * A025935 A077506 A007592
KEYWORD
nonn,easy
STATUS
approved