A085788 Partial sums of n 3-spaced triangular numbers beginning with t(3), e.g., a(2)=t(3)+t(6)=6+21=27.

6, 27, 72, 150, 270, 441, 672, 972, 1350, 1815, 2376, 3042, 3822, 4725, 5760, 6936, 8262, 9747, 11400, 13230, 15246, 17457, 19872, 22500, 25350, 28431, 31752, 35322, 39150, 43245, 47616, 52272, 57222, 62475, 68040, 73926, 80142, 86697, 93600, 100860, 108486

Offset

1,1

Links

Table of n, a(n) for n=1..41.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 3/2 * n*(n+1)^2 = 3 * A006002(n).

a(n) = Sum_{j=1..n} (j+n+1)*(n+1). - Zerinvary Lajos, Sep 10 2006

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: 3*x*(x+2) / (x-1)^4. - Colin Barker, Mar 17 2014

Maple

a:=n->sum(sum(sum(j-k+1, j=1..n), k=0..n), m=0..n): seq(a(n), n=1..45); # Zerinvary Lajos, May 30 2007

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {6, 27, 72, 150}, 50] (* Harvey P. Dale, Dec 14 2017 *)

Prog

(PARI) v=vector(40, i, i*(i+1)/2); s=0; forstep(i=3, 40, 3, s+=v[i]; print1(s", "))

Crossrefs

Cf. A004188, A006002.

Row sums of triangle A001283.

Cf. A254407. - Bruno Berselli, Jan 30 2015

Sequence in context: A190623 A305158 A273408 * A027276 A101970 A136105

Adjacent sequences: A085785 A085786 A085787 * A085789 A085790 A085791

Keyword

nonn,easy

Author

Jon Perry, Jul 23 2003

Extensions

Edited and more terms from Michel Marcus, Mar 17 2014

Status

approved