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A066804 Sum of diagonal elements and those below it for a square matrix of integers, starting with 1. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)