A158842 a(n) = 1 + n*(n+1)*(n-1)/2.

1, 1, 4, 13, 31, 61, 106, 169, 253, 361, 496, 661, 859, 1093, 1366, 1681, 2041, 2449, 2908, 3421, 3991, 4621, 5314, 6073, 6901, 7801, 8776, 9829, 10963, 12181, 13486, 14881, 16369, 17953, 19636, 21421, 23311, 25309, 27418, 29641, 31981, 34441, 37024, 39733, 42571, 45541, 48646

Offset: 0

Author

Gary W. Adamson & Roger L. Bagula, Mar 28 2009

Keywords

• nonn
• easy

Comments

Binomial transform of the sequence 1, 0, 3, 3, 0, 0, 0, ... .

Examples

			a(4) = 31 = sum of row 4 terms of triangle A158841: (13 + 9 + 6 + 3).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Row sums of A158841.

Programs

Magma

[1+ n*(n+1)*(n-1)/2: n in [1..50]]; // Vincenzo Librandi, Nov 16 2011

Maple

A158842 := proc(n)
        1+n*(n+1)*(n-1)/2 ;
end proc:
seq(A158842(n),n=0..30) ; # R. J. Mathar, Nov 05 2011

Mathematica

Table[1 + n*(n + 1)*(n - 1)/2, {n, 40}] (* and *) LinearRecurrence[{4, -6, 4, -1}, {1, 4, 13, 31}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2012 *)

Formula

a(n) = 1+A027480(n-1) for n>=1. - R. J. Mathar, Mar 28 2009

G.f.: 1-x*(-1-3*x^2+x^3) / (x-1)^4 . - R. J. Mathar, Nov 05 2011

E.g.f.: exp(x)*(1 + x^3/2 + 3*x^2/2). - Nikolaos Pantelidis, Feb 13 2023

Extensions

a(0)=1 prepended by Andrew Howroyd, Feb 14 2023