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A109020 (2*7^n - 3*3^n + 1)/6. 1
0, 1, 12, 101, 760, 5481, 38852, 273421, 1918320, 13441361, 94128892, 659020341, 4613496680, 32295539641, 226071966132, 1582513328861, 11077621999840, 77543440092321, 542804338926572, 3799631147326981, 26597420355811800, 186181949464251401, 1303273667170466212 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of incongruent integer-edged Heron triangles whose circumdiameter is the product of n distinct primes of shape 4k + 1.

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (11, -31, 21).

FORMULA

a(0)=0, a(1)=1, a(2)=12, a(n)=11*a(n-1)-31*a(n-2)+21*a(n-3) -- From Harvey P. Dale, Aug 10 2012

G.f.: (-x^2-x)/(21*x^3-31*x^2+11*x-1) -- From Harvey P. Dale, Aug 10 2012

MATHEMATICA

Table[(2*7^n-3*3^n+1)/6, {n, 0, 30}] (* or *) LinearRecurrence[{11, -31, 21}, {0, 1, 12}, 30] (* Harvey P. Dale, Aug 10 2012 *)

CROSSREFS

Sequence in context: A199681 A211403 A008547 * A099299 A344366 A304504

Adjacent sequences:  A109017 A109018 A109019 * A109021 A109022 A109023

KEYWORD

nonn

AUTHOR

Alex Fink and R. K. Guy, Aug 18 2005

STATUS

approved

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Last modified August 1 16:12 EDT 2021. Contains 346393 sequences. (Running on oeis4.)