Revision History for A144902
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#12 by Michael De Vlieger at Wed Jul 27 10:36:28 EDT 2022
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#11 by Michel Marcus at Wed Jul 27 02:45:08 EDT 2022
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#10 by G. C. Greubel at Wed Jul 27 02:11:30 EDT 2022
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#9 by G. C. Greubel at Wed Jul 27 02:11:25 EDT 2022
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| LINKS
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<a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,85,-134,154,-140,106,-65,29,-8,1).
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proposed
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#8 by G. C. Greubel at Wed Jul 27 02:01:51 EDT 2022
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#7 by G. C. Greubel at Wed Jul 27 02:01:05 EDT 2022
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| FORMULA
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From G. C. Greubel, Jul 27 2022: (Start)
a(n) = Sum_{j=0..floor((n+7)/3)} binomial(n-2*j+7, j+8).
a(n) = A099567(n+7, 8). (End)
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| MATHEMATICA
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CoefficientList[Series[x / ((/((1 - -x - -x^3) ()(1 - -x)^8), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
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| PROG
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(Magma)
A144903:= func< n | n eq 0 select 0 else (&+[Binomial(n-2*j+7, j+8): j in [0..Floor((n+7)/3)]]) >;
[A144903(n): n in [0..40]]; // G. C. Greubel, Jul 27 2022
(SageMath)
def A144903(n): return sum(binomial(n-2*j+7, j+8) for j in (0..((n+7)//3)))
[A144903(n) for n in (0..40)] # G. C. Greubel, Jul 27 2022
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| CROSSREFS
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Cf. A099567.
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approved
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#6 by Alois P. Heinz at Thu Jun 06 06:30:21 EDT 2013
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#5 by Alois P. Heinz at Thu Jun 06 06:30:10 EDT 2013
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| DATA
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0, 1, 9, 45, 166, 505, 1342, 3224, 7161, 14938, 29602, 56211, 102973, 182963, 316694, 535947, 889454, 1451305, 2333356, 3703510, 5812615, 9034001, 13921551, 21294946, 32364747, 48915873, 73576675, 110213470, 164508959, 244810154, 363371304, 538175735
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| MAPLE
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a := := n-> (Matrix(11, (i, , j)-> if i=j-1 then 1 elif j=1 then [9, -36, 85, -134, 154, -140, 106, -65, 29, -8, 1][i] else 0 fi)^n)[1, , 2]: seq ((a(n), n=0..40);
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proposed
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#4 by Vincenzo Librandi at Thu Jun 06 01:49:34 EDT 2013
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#3 by Vincenzo Librandi at Thu Jun 06 01:49:25 EDT 2013
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| LINKS
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Vincenzo Librandi, <a href="/A144902/b144902.txt">Table of n, a(n) for n = 0..1000</a>
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| MATHEMATICA
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CoefficientList[Series[x / ((1 - x - x^3) (1 - x)^8), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
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| KEYWORD
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nonn,easy
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| STATUS
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approved
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