%I A049450
%S A049450 0,2,10,24,44,70,102,140,184,234,290,352,420,494,574,660,752,850,954,
%T A049450 1064,1180,1302,1430,1564,1704,1850,2002,2160,2324,2494,2670,2852,
%U A049450 3040,3234,3434,3640,3852,4070,4294,4524,4760,5002,5250,5504,5764
%N A049450 Pentagonal numbers multiplied by 2: n*(3*n-1).
%C A049450 Write 1,2,3,4,... in a hexagonal spiral around 0, then a(n) is the sequence 
               found by reading the line from 0 in the direction 0,2,... - Floor 
               van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001. The spiral begins:
%C A049450 ......16..15..14
%C A049450 ....17..5...4...13
%C A049450 ..18..6...0...3...12
%C A049450 19..7...1...2...11..26
%C A049450 ..20..8...9...10..25
%C A049450 ....21..22..23..24
%C A049450 Twice pentagonal numbers. - Omar E. Pol (info(AT)polprimos.com), May 
               14 2008
%C A049450 Starting with offset 1 = binomial transform of [2, 8, 6, 0, 0, 0,...] 
               [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 09 2009]
%C A049450 Number of permutations of n distinct objects (ABC...) 1 times >>("-", 
               A, AB, ABC,... ABCDEFGHIJK, infinity) and one after the other to 
               resemble motif: AA (2), AAB (2-1), AABC (2-1-1),...AABCDEFG (2—1-1-1-1-1-1), 
               etc..., n-3 fixed point. Example: AB and motif:AA then 0* n-3 fixed 
               point. ABC and motif:AAB then 2* n-3 fixed point. ABCD and motif: 
               AABC then 10* (n-3) fixed point. ABCDE and motif AABCD then 24 (n-3) 
               fixed point. ABCDEF and motif AABCDE then 44 * (n-3) fixed point. 
               ABCDEFG and motif AABCDEF 70 * (n-3) fixed point. etc... [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Nov 29 2009]
%H A049450 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A049450 G.f.: A(x) = 2*x*(1+2*x)/(1-x)^3.
%F A049450 a(n)= A049452(n)-A033428(n), example: 102=210-108, etc... - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007
%F A049450 a(n)=A000326(n)*2. - Omar E. Pol (info(AT)polprimos.com), May 14 2008
%F A049450 a(n) = A022264(n) - A000217(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 09 2008]
%F A049450 a(n)=6*n+a(n-1)-10 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 08 2009]
%e A049450 For n=2, a(2)=6*2+0-10=2; n=3, a(3)=6*3+2-10=10; n=4, a(4)=6*4+10-10=24 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
%p A049450 a:=n->sum(n/3, j=2..n): seq(a(3*n), n=0..44); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 30 2007
%p A049450 seq(n*(3*n-1),n=0..44); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 12 2007
%t A049450 lst={};Do[AppendTo[lst, n*(3*n-1)], {n, 0, 5!}];lst ...and/or... s=0;
               lst={s};Do[s+=n+1;AppendTo[lst, s], {n, 1, 6!, 6}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
%Y A049450 Cf. A000567.
%Y A049450 Bisection of A001859. Cf. A045944, A000326, A033579, A027599, A049451.
%Y A049450 Sequence in context: A005962 A120548 A120845 this_sequence A092906 A130016 
               A120550
%Y A049450 Adjacent sequences: A049447 A049448 A049449 this_sequence A049451 A049452 
               A049453
%K A049450 nonn,easy,nice,new
%O A049450 0,2
%A A049450 Joe Keane (jgk(AT)jgk.org).