A132112 a(n) = n*(n+1)*(11*n+1)/6.

0, 4, 23, 68, 150, 280, 469, 728, 1068, 1500, 2035, 2684, 3458, 4368, 5425, 6640, 8024, 9588, 11343, 13300, 15470, 17864, 20493, 23368, 26500, 29900, 33579, 37548, 41818, 46400, 51305, 56544, 62128, 68068, 74375, 81060, 88134, 95608, 103493, 111800

Offset: 0

Author

Reinhard Zumkeller, Aug 10 2007

Keywords

• nonn
• easy

Comments

Sums of rows of the triangle in A132111.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000330, A033994, A050409, A132111, A132121, A132124, A254407.

Programs

Magma

I:=[0, 4, 23, 68]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 29 2012

Mathematica

CoefficientList[Series[x*(4+7*x)/(1-x)^4,{x,0,40}],x] (* Vincenzo Librandi, Jun 29 2012 *)
LinearRecurrence[{4,-6,4,-1},{0,4,23,68},40] (* Harvey P. Dale, Jun 28 2021 *)

PARI

a(n)=n*(n+1)*(11*n+1)/6 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = A132121(n,3) for n > 2.

G.f.: x*(4+7*x)/(1-x)^4. - Colin Barker, Jun 06 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 29 2012

a(-n) = -A254407(n-1). - Bruno Berselli, Jan 31 2015

E.g.f.: exp(x)*x*(24 + 45*x + 11*x^2)/6. - Stefano Spezia, Feb 21 2024