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A082106 Main diagonal of number array A082105. 2
1, 6, 33, 118, 321, 726, 1441, 2598, 4353, 6886, 10401, 15126, 21313, 29238, 39201, 51526, 66561, 84678, 106273, 131766, 161601, 196246, 236193, 281958, 334081, 393126, 459681, 534358, 617793, 710646, 813601, 927366, 1052673, 1190278 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

4*a(n) can be written as (n^2+2*n+1)^2 + (n^2-2*n+1)^2 + (n^2-2*n-1)^2 + (n^2+2*n-1)^2. [Bruno Berselli, Jun 20 2014]

LINKS

Table of n, a(n) for n=0..33.

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

FORMULA

a(n) = n^4 + 4*n^2 + 1.

a(0)=1, a(1)=6, a(2)=33, a(3)=118, a(4)=321; for n>4, a(n) = 5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Dec 06 2012

G.f.: (1 + x + 13*x^2 + 3*x^3 + 6*x^4)/(1 - x)^5. [Bruno Berselli, Jun 20 2014]

MATHEMATICA

Table[n^4+4n^2+1, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 6, 33, 118, 321}, 40] (* Harvey P. Dale, Dec 06 2012 *)

CROSSREFS

Cf. A082047, A082044.

Sequence in context: A204185 A057818 A063267 * A297392 A263479 A073375

Adjacent sequences:  A082103 A082104 A082105 * A082107 A082108 A082109

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Apr 03 2003

STATUS

approved

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Last modified April 21 01:03 EDT 2019. Contains 322310 sequences. (Running on oeis4.)