A066804 Sum of diagonal elements and those below it for a square matrix of integers, starting with 1.

1, 8, 34, 100, 235, 476, 868, 1464, 2325, 3520, 5126, 7228, 9919, 13300, 17480, 22576, 28713, 36024, 44650, 54740, 66451, 79948, 95404, 113000, 132925, 155376, 180558, 208684, 239975, 274660, 312976, 355168, 401489, 452200, 507570, 567876

Offset

1,2

References

T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

a(n) = n*(n+1)*(2*n^2-n+2)/6.

G.f.: x*(1+3*x+4*x^2)/(1-x)^5. [Bruno Berselli, Jun 22 2013]

a(n) = n*A000217(n) - sum((n-4*i)*A000217(i), i=0..n-1). [Bruno Berselli, Jun 22 2013]

a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4)+a(n-5), with n>4, a(0)=1, a(1)=8, a(2)=34, a(3)=100, a(4)=235. [Yosu Yurramendi, Sep 03 2013]

Example

a(7) = 7*28 - (7*0+3*1-1*3-5*6-9*10-13*15-17*21) = 868. [Bruno Berselli, Jun 22 2013]

Mathematica

Table[n(n+1)(2n^2-n+2)/6, {n, 50}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 8, 34, 100, 235}, 50] (* Harvey P. Dale, Dec 02 2016 *)

Prog

(Magma) [n*(n+1)*(2*n^2-n+2)/6: n in [1..30]]; // Vincenzo Librandi, May 22 2011
(R)
a <- c(1, 8, 34, 100, 235)
for(n in (length(a)+1):30) a[n] <- 5*a[n-1] -10*a[n-2] +10*a[n-3] -5*a[n-4]+a[n-5]
a
[Yosu Yurramendi, Sep 03 2013]

Crossrefs

Sequence in context: A301887 A208639 A240785 * A033455 A172202 A053298

Adjacent sequences: A066801 A066802 A066803 * A066805 A066806 A066807

Keyword

nonn,easy

Author

Aaron Gulliver (agullive(AT)ece.uvic.ca), Jan 19 2002

Extensions

More terms from Sascha Kurz, Mar 23 2002

Status

approved