Search: id:A079273
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%I A079273
%S A079273 1,10,29,58,97,146,205,274,353,442,541,650,769,898,1037,1186,1345,1514,
%T A079273 1693,1882,2081,2290,2509,2738,2977,3226,3485,3754,4033,4322,4621,4930,
%U A079273 5249,5578,5917,6266,6625,6994,7373,7762,8161,8570,8989,9418,9857,10306
%N A079273 Octo numbers (a polygonal sequence): 5n^2-6n+2, or (n-1)^2 + (2n-1)^2.
%C A079273 a(n+1) = a(n)+10n-1 and n+a(n) is always congruent to 2 mod 10 (notice 
               pattern of final digits). a(n)= the n-th hex number (3n^2-3n+1) added 
               to the (2n-2)nd triangular number (2n^2-3n+1). The formula for the 
               n-th octo number can be written as (2n-1)^2 + (n-1)^2; compare to 
               formula for n-th octagonal number, n(3n-2)= (2n-1)^2 - (n-1)^2.
%C A079273 a(n+1)=5n^2+4n+1 is also the number of ways of realizing the amount 10n 
               using only coins with values 1, 2 and 5. [From François Brunault 
               (brunault(AT)gmail.com), Nov 24 2009]
%H A079273 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HexNumber.html">Link to a section of The World Of Mathematics. </
               a> (on hex numbers)
%F A079273 a(n)=10*n+a(n-1)-11 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 10 2009]
%e A079273 a(4)=58 because 58 dots can be arranged into a simple octagonal pattern 
               with 4 dots on each side, its rows from top to bottom containing 
               4,5,6,7,7,7,7,6,5 and 4 dots respectively. The pattern is similar 
               to the pattern for hex numbers (see link), with the exception that 
               while the n-th hex figure has only 1 row of length 2n-1 dots (the 
               maximum length) in the center, the n-th octo figure has n such rows.
%e A079273 a(4) = 58:
%e A079273 .. O O O O
%e A079273 . O O O O O
%e A079273 .O O O O O O
%e A079273 O O O O O O O
%e A079273 O O O O O O O
%e A079273 O O O O O O O
%e A079273 O O O O O O O
%e A079273 .O O O O O O
%e A079273 . O O O O O
%e A079273 .. O O O O
%e A079273 For n=1, a(1)=1; n=2, a(2)=10; [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Feb 08 2009]
%e A079273 For n=2, a(2)=10*2+1-11=10; n=3, a(3)=10*3+10-11=29; n=4, a(4)=10*4+29-11=58 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 10 2009]
%Y A079273 Cf. A000217 (triangular numbers), A000567 (octagonal numbers), A003215 
               (hex numbers).
%Y A079273 Adjacent sequences: A079270 A079271 A079272 this_sequence A079274 A079275 
               A079276
%K A079273 easy,nonn,nice,new
%O A079273 1,2
%A A079273 Matthew Vandermast (ghodges14(AT)comcast.net), Feb 06 2003
%E A079273 First line of %F removed (wrong formula).Typo corrected in the next to 
               last line of %e (wrong values) François Brunault (brunault(AT)gmail.com), 
               Nov 24 2009

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