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

0,2

Comments

Row sums of the triangle in A245300.

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).

Formula

a(n) = n*(n+1)*(7*n+8)/6 = A002378(n)*A016993(n+1)/6.

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

Maple

A245301:= n-> n*(n+1)*(7*n+8)/6; seq(A245301(n), n=0..50); # G. C. Greubel, Mar 31 2021

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 *)

Prog

(Haskell)
a245301 n = n * (n * (7 * n + 15) + 8) `div` 6
(PARI) a(n)=n*(7*n^2+15*n+8)/6 \\ Charles R Greathouse IV, Feb 01 2016
(Magma) [n*(7*n^2+15*n+8)/6: n in [0..60]]; // Vincenzo Librandi, Feb 01 2016
(Sage) [n*(n+1)*(7*n+8)/6 for n in (0..50)] # G. C. Greubel, Mar 31 2021

Crossrefs

Cf. A002378, A016993, A245300, A254407.

Sequence in context: A301499 A033445 A208946 * A256971 A273685 A050533

Adjacent sequences: A245298 A245299 A245300 * A245302 A245303 A245304

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jul 17 2014

Status

approved