A245301 a(n) = n*(7*n^2 + 15*n + 8)/6.
0, 5, 22, 58, 120, 215, 350, 532, 768, 1065, 1430, 1870, 2392, 3003, 3710, 4520, 5440, 6477, 7638, 8930, 10360, 11935, 13662, 15548, 17600, 19825, 22230, 24822, 27608, 30595, 33790, 37200, 40832, 44693, 48790, 53130, 57720, 62567, 67678, 73060, 78720, 84665
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Haskell
a245301 n = n * (n * (7 * n + 15) + 8) `div` 6
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Magma
[n*(7*n^2+15*n+8)/6: n in [0..60]]; // Vincenzo Librandi, Feb 01 2016
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Maple
A245301:= n-> n*(n+1)*(7*n+8)/6; seq(A245301(n), n=0..50); # G. C. Greubel, Mar 31 2021
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Mathematica
Table[n (7 n^2 + 15 n + 8)/6, {n, 0, 50}] (* Vincenzo Librandi, Feb 01 2016 *) LinearRecurrence[{4,-6,4,-1},{0,5,22,58},50] (* Harvey P. Dale, Sep 21 2019 *) -
PARI
a(n)=n*(7*n^2+15*n+8)/6 \\ Charles R Greathouse IV, Feb 01 2016
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Sage
[n*(n+1)*(7*n+8)/6 for n in (0..50)] # G. C. Greubel, Mar 31 2021
Formula
a(n) = Sum_{j=0..n} A000217(2n-j)+j. - Manfred Arens, Dec 26 2015
G.f.: x*(5 + 2*x)/(1-x)^4. - Vincenzo Librandi, Feb 01 2016
E.g.f.: x*(30 + 36*x + 7*x^2)*exp(x)/6. - G. C. Greubel, Mar 31 2021
Comments